Opened 5 years ago
Last modified 5 years ago
#16652 new enhancement
expansion of psi(m/n)
Reported by: | rws | Owned by: | |
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Priority: | minor | Milestone: | sage-wishlist |
Component: | symbolics | Keywords: | special, psi, polygamma, expansion |
Cc: | Merged in: | ||
Authors: | Reviewers: | ||
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description
As example, expressions with several psi values of rational argument result from infinite sums:
sage: sum((-1)^(k+1)/(4*k-3), k, 1, oo) 1/8*psi(5/8) - 1/8*psi(1/8)
psi(m/n)
, m<k, has a closed form of finitely many terms of elementary functions, so differences of psi values can yield nice expressions like 1/8*psi(5/8) - 1/8*psi(1/8) = 1/(4*sqrt(2))*(pi+2*log(sqrt(2)+1))
To arrive at such simplifications the expansion of psi(m/n)
using Gauss' Digamma Theorem should be implemented.
https://en.wikipedia.org/wiki/Digamma_function#Gauss.27s_digamma_theorem
Change History (3)
comment:1 Changed 5 years ago by
- Keywords polygamma added; digamma removed
- Priority changed from major to minor
comment:2 Changed 5 years ago by
- Milestone changed from sage-6.3 to sage-6.4
comment:3 Changed 5 years ago by
- Milestone changed from sage-6.4 to sage-wishlist
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