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Merge pull request #7 from ckormanyos/update_docs_again
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Update docs even more
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ckormanyos authored Aug 30, 2023
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16 changes: 5 additions & 11 deletions README.md
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for brief mathematical insight into the fascinating
series expansion of the reciprocal of the gamma function near the origin.

The implementation uses the `gfortran` dialect that is available in `g++`.

## Run, Test and CI

The test run computes $9$ gamma values
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[short link](https://godbolt.org/z/Y3zdd6zd6)
to [godbolt](https://godbolt.org).

## Licensing and Original Implementation

The original `Fortran77` version of this routine is copyrighted by
Shanjie Zhang and Jianming Jin. See also the subroutine `GAMMA`
in Sect. 3.1.5 on pages 49-50 of [1].

The program has been modified for this repository.
- Use the `gfortran` dialect that is available in `g++`.
- Adapt argument/calculation/result to quadruple-precision using the `REAL*16` data type.
- Expand the small-argument series expansion to $48$ coefficients having $51$ decimal digit precision. These have been acquired from a computer algebra system.

## References

A similar `Fortran77` program based on double-precision arithmetic (`REAL*8`)
can be found in the subroutine `GAMMA` in Sect. 3.1.5 on pages 49-50 of [1].

[1] Shanjie Zhang and Jianming Jin, _Computation_ _of_ _Special_ _Functions_,
Wiley, 1996, ISBN: 0-471-11963-6, LC: QA351.C45

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