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Results tagged with special-functions
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user 359
Many special functions appear as solutions of differential equations or integrals of elementary functions. Most special functions have relationships with representation theory of Lie groups.
6
votes
A 2F1 Hypergeometric identity from a Feynman integral
Since you are using Mathematica, you definitely want to take a look at the extremely useful package HolonomicFunctions by Christoph Koutschan.
In your particular example,
Annihilator[f1[d], {S[d]}]
…
- 18.4k
8
votes
3
answers
1k
views
No simple duplication formula for factorials?
Many special functions including the gamma function have a duplication formula of some sorts. In the case of the gamma function it reads:
Gamma(2z) = Gamma(z) Gamma(z+1/2) 22z-1/Gamma(1/2)
On t …
- 13.5k
8
votes
Accepted
Proving a hypergeometric function identity
You can use the great HolonomicFunctions package by Christoph Koutschan to prove this identity in Mathematica. It automatically proves for you that both sides of your identity satisfy the sixth order …
- 1,412