
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.LanguascoPrograms
Pari/Gp scripts
A) specialfunct_packagefinal.gp:
Pari/Gp
script. It can be used via
gp2c.
Please read the description at the top of the gpfile.
Toward the bottom of the gpfile 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 Gfunction, 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 gpfile.
Toward the bottom of the gpfile 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, k_{1}, k_{2}), s>1 (for FFT applications; results saved on file);
it computes: ζ(s,(g^{k} mod q)/q) for k_{1}≤k≤k_{2};
2) zetahprime(s, k_{1}, k_{2}), s>1 (for FFT applications; results saved on file)
the first derivative of the Hurwitz ζ function: ζ'(s,(g^{k} mod q)/q) for k_{1}≤k≤k_{2};
3) zetahtotal(s, k_{1}, k_{2}), s>1 (for FFT applications; results saved on file);
ζ(s,(g^{k} mod q)/q) and ζ'(s,(g^{k} mod q)/q) for k_{1}≤k≤k_{2};
4) hurwitz_DIF_even (compute both ζHurwitz and ζ'Hurwitz with reflection fornulae;
even case; Propositions 5 and 6 of [1]; results saved on file);
it computes ζ(s,(g^{k} mod q)/q) + ζ(s,1(g^{k} mod q)/q) for k_{1}≤k≤k_{2} and
ζ'(s,(g^{k} mod q)/q) + ζ'(s,1(g^{k} mod q)/q) for k_{1}≤k≤k_{2};
5) hurwitz_DIF_odd (compute both ζHurwitz and ζ'Hurwitz with reflection fornulae;
odd case; Propositions 5 and 6 of [1]; results saved on file);
it computes ζ(s,(g^{k} mod q)/q)  ζ(s,1(g^{k} mod q)/q) for k_{1}≤k≤k_{2} and
ζ'(s,(g^{k} mod q)/q)  ζ'(s,1(g^{k} mod q)/q) for k_{1}≤k≤k_{2}.
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
