Alessandro Languasco

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Alessandro Languasco


Papers: List Papers; (with Abstracts); Curriculum (in Italian): long version ; short version); Google Scholar profile. ResearchGate page. Orcid ID. Scopus Author ID. Thomson Reuters Researcher ID, Mathematical Reviews page.


Programs and numerical results for the paper
``An unified strategy to compute some special functions''
by A. Languasco



In this page I include my programs (Pari/Gp scripts) developed to obtain the numerical results described in the paper [1].

I have to state the obvious fact that if you wish to use some of the softwares below for your own research, you should acknowledge the author and cite the relevant paper in which the program was used first. In other words, you can use them but you have to cite the paper of mine that contains such programs. If you are wondering why I am stating something so trivial, please have a look at P0 here: A.Languasco-Programs


Pari/Gp scripts
A) specialfunct_package-final.gp: Pari/Gp script. It can be used via gp2c. Please read the description at the top of the gp-file. Toward the bottom of the gp-file you will find some correctness and performances tests.
It contains several functions:
1) logΓ(x), for x>0;
2) ψ(x), for x>0;
3) Bateman G-function, for x>0;
4) Hurwitz ζ(s,x), for x>0, s>1, (in another file named hurwitz_forfft.gp there's version with x in (0,1) for FFT applications);
4*) ONLY in another file: Hurwitz ζ'(s,x),x in (0,1), s>1 (ONLY in another file hurwitz_forfft.gp there's version with x in (0,1) for FFT applications);
5) Dirichlet β(s), s>1;
6) Dirichlet β'(s), s>1;
7) Dirichlet β values (s), s>1 (it computes β'/ β(s), β(s) and β'(s) at the same time);
8) Catalan constant computation.
B) hurwitz_forfft.gp: Pari/Gp script. It can be used via gp2c. Please read the description at the top of the gp-file. Toward the bottom of the gp-file you will find some correctness and performances tests. All these programs require in input a file named primroot.res containing:
on the first line: a prime number q; on the second line: a primitive root g of q.
It contains several functions:
1) zetah(s, k1, k2), s>1 (for FFT applications; results saved on file); it computes: ζ(s,(gk mod q)/q) for k1≤k≤k2;
2) zetahprime(s, k1, k2), s>1 (for FFT applications; results saved on file) the first derivative of the Hurwitz ζ function: ζ'(s,(gk mod q)/q) for k1≤k≤k2;
3) zetahtotal(s, k1, k2), s>1 (for FFT applications; results saved on file); ζ(s,(gk mod q)/q) and ζ'(s,(gk mod q)/q) for k1≤k≤k2;
4) hurwitz_DIF_even (compute both ζ-Hurwitz and ζ'-Hurwitz with reflection fornulae; even case; Propositions 5 and 6 of [1]; results saved on file);
it computes ζ(s,(gk mod q)/q) + ζ(s,1-(gk mod q)/q) for k1≤k≤k2 and ζ'(s,(gk mod q)/q) + ζ'(s,1-(gk mod q)/q) for k1≤k≤k2;
5) hurwitz_DIF_odd (compute both ζ-Hurwitz and ζ'-Hurwitz with reflection fornulae; odd case; Propositions 5 and 6 of [1]; results saved on file);
it computes ζ(s,(gk mod q)/q) - ζ(s,1-(gk mod q)/q) for k1≤k≤k2 and ζ'(s,(gk mod q)/q) - ζ'(s,1-(gk mod q)/q) for k1≤k≤k2.

References

Some of the mathematical papers connected with this project are the following.
[1] A. Languasco - An unified strategy to compute some special functions - preprint, 2022.



Ultimo aggiornamento: 05.01.2022: 17:34:12

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