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ckormanyos committed Mar 19, 2024
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<img src="https://img.shields.io/badge/try%20it%20on-godbolt-green" /></a>
</p>

gamma_f77 implements the real-valued Gamma function in quadruple-precision using
the classic `Fortran77` language.
`ckormanyos/gamma_f77` implements the real-valued Gamma function
in quadruple-precision using the classic `Fortran77` language.

## Mathematical Background

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$$ \frac{1}{\Gamma(z)}\approx \sum_{k=1}^{n} a^{k} z^{k}\text{.}$$

Let's look at some background information.

In the subroutine `GAMMA` in Sect. 3.1.5 on pages 49-50 of [1],
the coefficients $a_{k}$ are given to $26$ terms. These are used
in a series calculation of $\Gamma\left(x\right)$ for real-valued $x$
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for brief mathematical insight into the fascinating
series expansion of the reciprocal of the gamma function near the origin.

## Quadruple-Precision Implementation
## Expanded Quadruple-Precision Implementation

In this repository, the series calculation mentioned above has been
extended to quadruple-precision.
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