# abax
A lightweight Rust library providing high-precision mathematical constants and special functions.
## Features
- **Mathematical Constants**:
- Bernoulli numbers (<math><msub><mi>B</mi><mrow><mn>2</mn><mi>n</mi></mrow></msub></math>) up to <math><mi>n</mi><mo>=</mo><mn>16</mn></math>.
- Riemann Zeta function values for integers <math><mn>2</mn></math> through <math><mn>16</mn></math>.
- Euler-Mascheroni constant.
- Stirling series coefficients for asymptotic expansions.
- **Special Functions**:
- `gamma(x)`: Gamma function <math><mi>Γ</mi><mo>(</mo><mi>x</mi><mo>)</mo></math> computed with the Lanczos approximation and reflection formula.
- `gammaln(x)`: Natural logarithm of the Gamma function <math><mi>ln</mi><mo>(</mo><mi>Γ</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></math> using Stirling's approximation for high precision.
- `digamma(x)`: Digamma function <math><mi>ψ</mi><mo>(</mo><mi>x</mi><mo>)</mo></math>, the logarithmic derivative of <math><mi>Γ</mi><mo>(</mo><mi>x</mi><mo>)</mo></math>, implemented with reflection, recurrence shifting, and asymptotic expansion for numerical stability.
- `trigamma(x)`: Trigamma function <math><msup><mi>ψ</mi><mo>(</mo><mn>1</mn><mo>)</mo></msup><mo>(</mo><mi>x</mi><mo>)</mo></math>, implemented with reflection, recurrence shifting, and asymptotic expansion for numerical stability.
- `tetragamma(x)`: Tetragamma function <math><msup><mi>ψ</mi><mo>(</mo><mn>2</mn><mo>)</mo></msup><mo>(</mo><mi>x</mi><mo>)</mo></math>, implemented with reflection, recurrence shifting, and asymptotic expansion for numerical stability.
- `gammainc(x, a, lower, scaled)`: Regularized lower/upper incomplete gamma function with explicit lower/upper tail selection; when `scaled=true`, returns tail value multiplied by <math><mi>Γ</mi><mo>(</mo><mi>a</mi><mo>+</mo><mn>1</mn><mo>)</mo><msup><mi>e</mi><mi>x</mi></msup><msup><mi>x</mi><mrow><mo>-</mo><mi>a</mi></mrow></msup></math> for improved conditioning at large <math><mi>x</mi></math>.
- `gammaincinv(y, a, lower)`: Numerically robust inverse of the regularized incomplete gamma function utilizing a combined Halley-Newton-Bisection method for enhanced convergence speed and stability in tail regions.
- `psi(k, x)`: Polygamma interface returning <math><msup><mi>ψ</mi><mo>(</mo><mi>k</mi><mo>)</mo></msup><mo>(</mo><mi>x</mi><mo>)</mo></math> with stable handling of poles and infinities.
## Usage
Add this to your `Cargo.toml`:
```toml
[dependencies]
abax = "0.1.8"
```
## License
This project is licensed under the MIT License - see the LICENSE file for details.
## Repository
Source code is available on GitHub.