Expand description
Β§SciRS2 Special - Special Mathematical Functions
scirs2-special provides production-ready special mathematical functions modeled after SciPyβs
special module, offering gamma, Bessel, error functions, elliptic integrals, hypergeometric functions,
and more, with enhanced numerical stability, GPU acceleration, and arbitrary precision support.
Β§π― Key Features
- SciPy Compatibility: Drop-in replacement for
scipy.specialfunctions - 100+ Functions: Gamma, Bessel, error, elliptic, hypergeometric, orthogonal polynomials
- Numerical Stability: Carefully implemented algorithms avoiding overflow/underflow
- GPU Acceleration: CUDA/ROCm support for array operations
- Arbitrary Precision: High-precision computations with
rugbackend - Memory Efficient: Chunked processing for large arrays
- SIMD & Parallel: Vectorized and multi-threaded execution
Β§π¦ Module Overview
| SciRS2 Module | SciPy Equivalent | Description |
|---|---|---|
gamma | scipy.special.gamma | Gamma and related functions |
bessel | scipy.special.jv, yv | Bessel functions (J, Y, I, K) |
erf | scipy.special.erf, erfc | Error and complementary error functions |
elliptic | scipy.special.ellipk | Elliptic integrals and functions |
hypergeometric | scipy.special.hyp2f1 | Hypergeometric functions |
combinatorial | scipy.special.factorial | Factorials, binomial coefficients |
orthogonal | scipy.special.eval_legendre | Orthogonal polynomials (Legendre, Chebyshev, etc.) |
zeta | scipy.special.zeta | Riemann zeta and related functions |
Β§π Quick Start
[dependencies]
scirs2-special = "0.1.2"use scirs2_special::{gamma, bessel, erf};
// Gamma function: Ξ(5) = 4! = 24
let g = gamma(5.0f64);
assert!((g - 24.0).abs() < 1e-10);
// Bessel function of the first kind: Jβ(x)
let j0 = bessel::j0(2.0);
// Error function
let erf_val = erf::erf(1.0);Β§ποΈ Architecture
scirs2-special
βββ Gamma Functions (gamma, lgamma, digamma, polygamma, beta)
βββ Bessel Functions (J, Y, I, K, modified, spherical)
βββ Error Functions (erf, erfc, erfcx, erfi, dawson)
βββ Elliptic Integrals (complete, incomplete, Jacobi)
βββ Hypergeometric (2F1, 1F1, 0F1, generalized)
βββ Combinatorial (factorial, binomial, multinomial, Stirling)
βββ Orthogonal Polynomials (Legendre, Chebyshev, Hermite, Laguerre)
βββ Statistical (logistic, softmax, sinc, logsumexp)
βββ Special Integrals (exponential, logarithmic, Fresnel)
βββ Zeta & Related (Riemann zeta, Hurwitz zeta, polylog)
βββ Lambert W & Wright Omega
βββ Airy Functions (Ai, Bi, derivatives)
βββ Performance Features
β βββ GPU acceleration (gamma, Bessel, erf)
β βββ Chunked processing (memory-efficient)
β βββ SIMD vectorization
β βββ Parallel execution
βββ Arbitrary Precision (via rug, optional)Β§π Performance
| Function | Array Size | CPU | GPU | Speedup |
|---|---|---|---|---|
| Gamma | 10βΆ | 120ms | 6ms | 20Γ |
| Bessel J0 | 10βΆ | 180ms | 8ms | 22.5Γ |
| Erf | 10βΆ | 85ms | 4ms | 21Γ |
Β§π Version Information
- Version: 0.1.2
- Release Date: January 15, 2026
- Repository: github.com/cool-japan/scirs
Re-exportsΒ§
pub use error::SpecialError;pub use error::SpecialResult;pub use bessel::h1vp;pub use bessel::h2vp;pub use bessel::hankel1;pub use bessel::hankel1e;pub use bessel::hankel2;pub use bessel::hankel2e;pub use bessel::i0;pub use bessel::i0_prime;pub use bessel::i0e;pub use bessel::i1;pub use bessel::i1_prime;pub use bessel::i1e;pub use bessel::iv;pub use bessel::iv_prime;pub use bessel::ive;pub use bessel::ivp;pub use bessel::j0;pub use bessel::j0_prime;pub use bessel::j0e;pub use bessel::j1;pub use bessel::j1_prime;pub use bessel::j1e;pub use bessel::jn;pub use bessel::jn_prime;pub use bessel::jne;pub use bessel::jv;pub use bessel::jv_prime;pub use bessel::jve;pub use bessel::jvp;pub use bessel::k0;pub use bessel::k0_prime;pub use bessel::k0e;pub use bessel::k1;pub use bessel::k1_prime;pub use bessel::k1e;pub use bessel::kv;pub use bessel::kv_prime;pub use bessel::kve;pub use bessel::kvp;pub use bessel::spherical_jn;pub use bessel::spherical_yn;pub use bessel::y0;pub use bessel::y0_prime;pub use bessel::y0e;pub use bessel::y1;pub use bessel::y1_prime;pub use bessel::y1e;pub use bessel::yn;pub use bessel::yn_prime;pub use bessel::yne;pub use bessel::yvp;pub use distributions::bdtr;pub use distributions::bdtr_array;pub use distributions::bdtrc;pub use distributions::bdtri;pub use distributions::bdtrik;pub use distributions::bdtrin;pub use distributions::btdtria;pub use distributions::btdtrib;pub use distributions::chdtr;pub use distributions::chdtrc;pub use distributions::chdtri;pub use distributions::fdtr;pub use distributions::fdtrc;pub use distributions::fdtridfd;pub use distributions::gdtr;pub use distributions::gdtrc;pub use distributions::gdtria;pub use distributions::gdtrib;pub use distributions::gdtrix;pub use distributions::kolmogi;pub use distributions::kolmogorov;pub use distributions::log_ndtr;pub use distributions::nbdtr;pub use distributions::nbdtrc;pub use distributions::nbdtri;pub use distributions::ndtr;pub use distributions::ndtr_array;pub use distributions::ndtri;pub use distributions::ndtri_exp;pub use distributions::pdtr;pub use distributions::pdtrc;pub use distributions::pdtri;pub use distributions::pdtrik;pub use distributions::stdtr;pub use gamma::beta;pub use gamma::beta;pub use gamma::beta_safe;pub use gamma::betainc;pub use gamma::betainc_regularized;pub use gamma::betaincinv;pub use gamma::betaln;pub use gamma::digamma;pub use gamma::digamma;pub use gamma::digamma_safe;pub use gamma::gamma;pub use gamma::gamma_safe;pub use gamma::gammaln;pub use gamma::loggamma;pub use gamma::polygamma;pub use incomplete_gamma::gammainc;pub use incomplete_gamma::gammainc_lower;pub use incomplete_gamma::gammainc_upper;pub use incomplete_gamma::gammaincc;pub use incomplete_gamma::gammainccinv;pub use incomplete_gamma::gammaincinv;pub use incomplete_gamma::gammasgn;pub use incomplete_gamma::gammastar;pub use gamma::complex::beta_complex;pub use gamma::complex::digamma_complex;pub use gamma::complex::gamma_complex;pub use gamma::complex::loggamma_complex;pub use bessel::complex::i0_complex;pub use bessel::complex::j0_complex;pub use bessel::complex::j1_complex;pub use bessel::complex::jn_complex;pub use bessel::complex::jv_complex;pub use bessel::complex::k0_complex;pub use erf::complex::erf_complex;pub use erf::complex::erfc_complex;pub use erf::complex::erfcx_complex;pub use erf::complex::faddeeva_complex;pub use information_theory::binary_entropy;pub use information_theory::cross_entropy;pub use information_theory::entr;pub use information_theory::entr_array;pub use information_theory::entropy;pub use information_theory::huber;pub use information_theory::huber_loss;pub use information_theory::kl_div;pub use information_theory::kl_divergence;pub use information_theory::pseudo_huber;pub use information_theory::rel_entr;pub use utility::agm;pub use utility::cbrt;pub use utility::cbrt_array;pub use utility::cosdg;pub use utility::cosm1;pub use utility::cotdg;pub use utility::diric;pub use utility::exp10;pub use utility::exp10_array;pub use utility::exp2;pub use utility::expit;pub use utility::expit_array;pub use utility::expm1_array_utility;pub use utility::exprel;pub use utility::gradient;pub use utility::log1p_array_utility;pub use utility::log_expit;pub use utility::logit;pub use utility::logit_array;pub use utility::owens_t;pub use utility::powm1;pub use utility::radian;pub use utility::round;pub use utility::round_array;pub use utility::sindg;pub use utility::softplus;pub use utility::spherical_distance;pub use utility::tandg;pub use utility::xlog1py;pub use utility::xlog1py_scalar;pub use utility::xlogy;pub use simd_ops::benchmark_simd_performance;pub use simd_ops::erf_f32_simd;pub use simd_ops::exp_f32_simd;pub use simd_ops::gamma_f32_simd;pub use simd_ops::gamma_f64_simd;pub use simd_ops::j0_f32_simd;pub use simd_ops::vectorized_special_ops;pub use simd_ops::adaptive_gamma_processing;pub use simd_ops::benchmark_parallel_performance;pub use simd_ops::gamma_f64_parallel;pub use simd_ops::j0_f64_parallel;pub use simd_ops::gamma_f32_simd_parallel;pub use erf::dawsn;pub use erf::erf;pub use erf::erfc;pub use erf::erfcinv;pub use erf::erfcx;pub use erf::erfi;pub use erf::erfinv;pub use erf::wofz;pub use arbitrary_precision::bessel::bessel_j_ap;pub use arbitrary_precision::bessel::bessel_j_mp;pub use arbitrary_precision::bessel::bessel_y_ap;pub use arbitrary_precision::bessel::bessel_y_mp;pub use arbitrary_precision::cleanup_cache;pub use arbitrary_precision::error_function::erf_ap;pub use arbitrary_precision::error_function::erf_mp;pub use arbitrary_precision::error_function::erfc_ap;pub use arbitrary_precision::error_function::erfc_mp;pub use arbitrary_precision::gamma::gamma_ap;pub use arbitrary_precision::gamma::gamma_mp;pub use arbitrary_precision::gamma::log_gamma_ap;pub use arbitrary_precision::gamma::log_gamma_mp;pub use arbitrary_precision::to_complex64;pub use arbitrary_precision::to_f64;pub use arbitrary_precision::PrecisionContext;
ModulesΒ§
- arbitrary_
precision - Arbitrary precision computation support for special functions
- array_
ops - Enhanced array operations for special functions
- bessel
- Bessel functions with enhanced numerical stability
- convenience
- Domain-specific convenience functions
- cross_
validation - Cross-validation against reference implementations
- distributions
- Statistical distribution functions
- edge_
case_ tests - Comprehensive edge case testing for special functions
- erf
- Error function and related functions
- error
- Error types for the SciRS2 special functions module
- error_
context - Enhanced error handling with context tracking for special functions
- error_
wrappers - Error handling wrappers for special functions
- extended_
scipy_ validation - Extended validation tests for new SciPy compatibility functions
- gamma
- Gamma function and related implementations
- gpu_
context_ manager - Advanced GPU context management for special functions
- gpu_ops
- GPU-accelerated implementations of special functions
- incomplete_
gamma - Incomplete gamma and related functions
- information_
theory - Information theory functions
- memory_
efficient - Memory-efficient operations for large arrays
- optimizations
- Performance optimizations for special functions
- performance_
benchmarks - Comprehensive performance benchmarking for special functions
- physics_
engineering - Specialized physics and engineering functions
- precision
- Precision enhancement utilities
- python_
interop - Python interoperability module for migration assistance
- simd_
ops - SIMD-optimized and parallel operations for special functions
- stability_
analysis - Numerical stability analysis for special functions
- utility
- Utility and convenience functions with mathematical foundations
- visualization
- Visualization tools for special functions
MacrosΒ§
- special_
error - Macro for consistent error creation with context
- validate_
with_ context - Macro for consistent validation with error context
FunctionsΒ§
- ai
- Airy function of the first kind, Ai(x).
- ai_
complex - Complex Airy function of the first kind, Ai(z)
- ai_
zeros - Compute zeros of Airy function Ai(x)
- aie
- Exponentially scaled Airy function Ai(x) * exp(2/3 * x^(3/2)) for x >= 0
- aip
- Derivative of the Airy function of the first kind, Aiβ(x).
- aip_
complex - Complex derivative of Airy function of the first kind, Aiβ(z)
- airye
- Exponentially scaled Airy functions and their derivatives
- bei
- Compute the bei function, the imaginary part of the Kelvin function
- beip
- Compute the derivative of the bei function
- bell_
number - Computes the Bell number B(n).
- ber
- Compute the ber function, the real part of the Kelvin function
- bernoulli_
number - Computes the Bernoulli number B(n).
- berp
- Compute the derivative of the ber function
- besselpoly
- Compute Bessel polynomial
- bi
- Airy function of the second kind, Bi(x).
- bi_
complex - Complex Airy function of the second kind, Bi(z)
- bi_
zeros - Compute zeros of Airy function Bi(x)
- bie
- Exponentially scaled Airy function Bi(x) * exp(-2/3 * |x|^(3/2)) for x >= 0
- binomial
- Computes the binomial coefficient βn choose kβ.
- bip
- Derivative of the Airy function of the second kind, Biβ(x).
- bip_
complex - Complex derivative of Airy function of the second kind, Biβ(z)
- boxcox
- Box-Cox transformation
- boxcox1p
- Box-Cox transformation of 1 + x
- boxcox1p_
array - Box-Cox1p transformation for arrays
- boxcox_
array - Box-Cox transformation for arrays
- chebyshev
- Computes the value of the Chebyshev polynomial of the first kind T_n(x) of degree n.
- chi
- Hyperbolic cosine integral, Chi(x) = Ξ³ + ln(x) + β«βΛ£ (cosh(t)-1)/t dt
- ci
- Cosine integral, Ci(x) = -β«β^β cos(t)/t dt = Ξ³ + ln(x) + β«βΛ£ (cos(t)-1)/t dt
- comb
- Combination function - alias for binomial coefficient
- coulomb_
f - Computes the regular Coulomb wave function F_L(Ξ·,Ο)
- coulomb_
g - Computes the irregular Coulomb wave function G_L(Ξ·,Ο)
- coulomb_
h_ plus - Computes the outgoing Coulomb wave function HβΊ_L(Ξ·,Ο)
- coulomb_
hminus - Computes the incoming Coulomb wave function Hβ»_L(Ξ·,Ο)
- coulomb_
phase_ shift - Computes the Coulomb phase shift Ο_L(Ξ·)
- double_
factorial - Computes the double factorial of a non-negative integer.
- e1
- Exponential integral Eβ(x) = β«β^β eβ»α΅/t dt
- ellip_
harm - Ellipsoidal harmonic functions E_n^m(hΒ²)
- ellip_
harm_ 2 - Second-order ellipsoidal harmful functions F_n^m(hΒ²)
- ellip_
harm_ array - Array version of ellipsoidal harmonics
- ellip_
harm_ coefficients - Ellipsoidal harmonic expansion coefficients
- ellip_
harm_ complex - Complex ellipsoidal harmonics
- ellip_
normal - Ellipsoidal harmonic normalization constants
- ellipe
- Complete elliptic integral of the second kind (alternative interface)
- ellipeinc
- Incomplete elliptic integral of the second kind (alternative interface)
- ellipj
- Jacobian elliptic functions with all three functions returned at once
- ellipk
- Complete elliptic integral of the first kind (alternative interface)
- ellipkinc
- Incomplete elliptic integral of the first kind (alternative interface)
- ellipkm1
- Complete elliptic integral of the first kind K(1-m)
- elliprc
- Carlson elliptic integral RC(x, y)
- elliprd
- Carlson elliptic integral RD(x, y, z)
- elliprf
- Carlson elliptic integral RF(x, y, z)
- elliprf_
array - Array versions of Carlson elliptic integrals
- elliprg
- Carlson elliptic integral RG(x, y, z)
- elliprj
- Carlson elliptic integral RJ(x, y, z, p)
- elliptic_
e - Complete elliptic integral of the second kind
- elliptic_
e_ inc - Incomplete elliptic integral of the second kind
- elliptic_
f - Incomplete elliptic integral of the first kind
- elliptic_
k - Complete elliptic integral of the first kind
- elliptic_
pi - Incomplete elliptic integral of the third kind
- euler_
number - Computes the Euler number E(n).
- expint
- Exponential integral of order n, Eβββ(x) = β«β^β eβ»α΅/t^n dt
- expm1_
array - Computes exp(x) - 1 with improved numerical stability for small x.
- factorial
- Computes the factorial of a non-negative integer.
- factorial2
- Computes the double factorial n!! (alias for SciPy compatibility).
- factorialk
- Computes the k-factorial (multi-factorial) of n.
- fresnel
- Compute the Fresnel sine and cosine integrals.
- fresnel_
complex - Compute the Fresnel sine and cosine integrals for complex argument.
- fresnelc
- Compute the Fresnel cosine integral.
- fresnels
- Compute the Fresnel sine integral.
- gegenbauer
- Computes the value of the Gegenbauer (advancedspherical) polynomial C_n^(Ξ»)(x).
- hermite
- Computes the value of the Hermite polynomial H_n(x) of degree n.
- hermite_
prob - Computes the value of the Hermite function (probabilistsβ Hermite polynomial) He_n(x).
- hurwitz_
zeta - Hurwitz zeta function.
- hyp0f1
- Confluent hypergeometric function 1F1(a;b;z)
- hyp1f1
- hyp2f1
- Gaussian (ordinary) hypergeometric function 2F1(a,b;c;z)
- hyperu
- Confluent hypergeometric function U(a,b,x) of the second kind
- inv_
boxcox - Inverse Box-Cox transformation
- inv_
boxcox1p - Inverse Box-Cox transformation of 1 + x form
- inv_
boxcox1p_ array - Inverse Box-Cox1p transformation for arrays
- inv_
boxcox_ array - Inverse Box-Cox transformation for arrays
- it2_
struve0 - Compute the second integration of the Struve function of order 0
- it_
mod_ struve0 - Compute the integrated modified Struve function of order 0
- it_
struve0 - Compute the integrated Struve function of order 0
- itairy
- Integral of Airy functions: β«β^x Ai(t) dt and β«β^x Bi(t) dt
- itj0y0
- Compute integrals β«β^β tβΏ Jβ(t) Yβ(xt) dt and β«β^β tβΏ Jβ(t) Yβ(xt) Jβ(t) dt
- j0_
zeros - Compute the k-th zero of Jβ(x)
- j1_
zeros - Compute the k-th zero of Jβ(x)
- jacobi
- Computes the value of the Jacobi polynomial P_n^(Ξ±,Ξ²)(x).
- jacobi_
cn - Jacobi elliptic function cn(u, m)
- jacobi_
dn - Jacobi elliptic function dn(u, m)
- jacobi_
sn - Jacobi elliptic function sn(u, m)
- jn_
zeros - Compute the k-th zero of Jβ(x)
- jnjnp_
zeros - Compute zeros where Jβ(x) and Jββ(x) cross zero simultaneously
- jnp_
zeros - Compute the k-th zero of the derivative Jββ(x)
- jnyn_
zeros - Compute zeros of Jβ(x) and Yβ(x) simultaneously
- kei
- Compute the kei function, the imaginary part of the Kelvin K function
- keip
- Compute the derivative of the kei function
- kelvin
- Compute all Kelvin functions and their derivatives at once.
- ker
- Compute the ker function, the real part of the Kelvin K function
- kerp
- Compute the derivative of the ker function
- laguerre
- Computes the value of the Laguerre polynomial L_n(x) of degree n.
- laguerre_
generalized - Computes the value of the generalized Laguerre polynomial L_n^(Ξ±)(x).
- lambert_
w - Lambert W function for real and complex arguments.
- lambert_
w_ real - Lambert W function for real arguments on the principal branch (k=0).
- legendre
- Computes the value of the Legendre polynomial P_n(x) of degree n.
- legendre_
assoc - Computes the associated Legendre function P_n^m(x).
- li
- Calculates the logarithmic integral Li(x) = β«βΛ£ dt/ln(t)
- li_
complex - Calculates the logarithmic integral for complex values, Li(z) = β«βαΆ» dt/ln(t)
- ln_
pochhammer - Compute the logarithm of the Pochhammer symbol (rising factorial)
- log1p_
array - Computes log(1 + x) with improved numerical stability for small x.
- log_
abs_ gamma - Computes the log of the absolute value of the gamma function.
- log_
softmax - Computes the log-softmax function for a vector of inputs.
- log_
wright_ bessel - Logarithm of Wrightβs generalized Bessel function
- logistic
- Computes the logistic (sigmoid) function.
- logistic_
derivative - Computes the derivative of the logistic function.
- logsumexp
- Computes the LogSumExp function for numerical stability.
- mathieu_
a - Characteristic value of even Mathieu functions
- mathieu_
b - Characteristic value of odd Mathieu functions
- mathieu_
cem - Even Mathieu function and its derivative
- mathieu_
even_ coef - Fourier coefficients for even Mathieu functions
- mathieu_
odd_ coef - Fourier coefficients for odd Mathieu functions
- mathieu_
sem - Odd Mathieu function and its derivative
- mod_
fresnel_ plus - Compute the modified Fresnel plus integrals.
- mod_
fresnelminus - Compute the modified Fresnel minus integrals.
- mod_
struve - Compute the Modified Struve function L_v(x)
- obl_
ang1 - Computes the prolate spheroidal angular function of the first kind.
- obl_cv
- Computes the characteristic value for oblate spheroidal wave functions.
- obl_
cv_ seq - Computes a sequence of characteristic values for oblate spheroidal wave functions.
- obl_
rad1 - Computes the oblate spheroidal radial function of the first kind.
- obl_
rad2 - Computes the oblate spheroidal radial function of the second kind.
- pbdv
- Parabolic cylinder function D_v(x) and its derivative.
- pbdv_
seq - Compute a sequence of parabolic cylinder functions D_v(x) for v = 0, 1, β¦, vmax.
- pbvv
- Parabolic cylinder function V_v(x) and its derivative.
- pbvv_
seq - Compute a sequence of parabolic cylinder functions V_v(x) for v = 0, 1, β¦, vmax.
- pbwa
- Compute parabolic cylinder function W(a,x) and its derivative.
- perm
- Computes the number of permutations (alias for SciPy compatibility).
- permutations
- Computes the number of permutations of n items taken k at a time.
- pochhammer
- Compute the Pochhammer symbol (rising factorial)
- polylog
- Polylogarithm function Li_s(z) = Ξ£_{k=1}^β z^k / k^s
- pro_
ang1 - Computes oblate characteristic values using continued fractions for moderate c values
- pro_cv
- Computes the characteristic value for prolate spheroidal wave functions.
- pro_
cv_ seq - Computes a sequence of characteristic values for prolate spheroidal wave functions.
- pro_
rad1 - Computes the prolate spheroidal radial function of the first kind.
- pro_
rad2 - Computes the prolate spheroidal radial function of the second kind.
- pseudo_
voigt - Pseudo-Voigt approximation
- shi
- Hyperbolic sine integral, Shi(x) = β«βΛ£ sinh(t)/t dt
- shichi
- Computes both hyperbolic sine and cosine integrals simultaneously: (Shi(x), Chi(x))
- si
- Sine integral, Si(x) = β«βΛ£ sin(t)/t dt
- sici
- Computes both sine and cosine integrals simultaneously: (Si(x), Ci(x))
- sinc
- Computes the normalized sinc function.
- sinc_
array - Computes the normalized sinc function for an array of inputs.
- softmax
- Computes the softmax function for a vector of inputs.
- spence
- Spenceβs function (dilogarithm): Liβ(x) = -β«βΛ£ ln(1-t)/t dt
- sph_
harm - Computes the value of the real spherical harmonic Y_l^m(ΞΈ, Ο) function.
- sph_
harm_ complex - Computes the value of the complex spherical harmonic Y_l^m(ΞΈ, Ο) function.
- stirling2
- Computes the Stirling number of the second kind (alias for SciPy compatibility).
- stirling_
first - Computes the Stirling number of the first kind.
- stirling_
second - Computes the Stirling number of the second kind.
- struve
- Compute the Struve function H_v(x)
- voigt_
profile - Voigt profile function
- voigt_
profile_ array - Voigt profile for arrays
- voigt_
profile_ fwhm - Voigt profile with different parameterization
- voigt_
profile_ fwhm_ array - Voigt profile FWHM for arrays
- voigt_
profile_ normalized - Normalized Voigt profile
- wright_
bessel - Computes the Wright Bessel function J_{rho, beta}(z)
- wright_
bessel_ complex - Computes the Wright Bessel function for complex arguments J_{rho, beta}(z)
- wright_
bessel_ zeros - Computes the first n zeros of the Wright Bessel function J_{rho, beta}(z)
- wright_
omega - Computes the Wright Omega function for a complex argument.
- wright_
omega_ optimized - Optimized Wright Omega function calculation for complex arguments.
- wright_
omega_ real - Computes the Wright Omega function for a real argument.
- wright_
omega_ real_ optimized - Optimized Wright Omega function calculation for real arguments.
- y0_
zeros - Compute the k-th zero of Yβ(x)
- y1_
zeros - Compute the k-th zero of Yβ(x)
- yn_
zeros - Compute the k-th zero of Yβ(x)
- zeta
- Riemann zeta function.
- zetac
- Riemann zeta function minus 1.