#6961: provide wrapper for psi function of GiNaC
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Reporter: burcin | Owner:
Type: enhancement | Status:
positive_review
Priority: major | Milestone: sage-4.3.3
Component: symbolics | Keywords: psi, gamma,
digamma, polygamma
Author: Burcin Erocal | Upstream: N/A
Reviewer: Karl-Dieter Crisman, Ross Kyprianou | Merged:
Work_issues: needs rebase on top of #6207 |
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Changes (by rossk):
* keywords: => psi, gamma, digamma, polygamma
* reviewer: => Karl-Dieter Crisman, Ross Kyprianou
* status: needs_review => positive_review
Comment:
{{{
sage: diff(gamma(x),x)/gamma(x) # definition of digamma (or "psi")
psi(x)
sage: diff(gamma(x),x).subs(x=1)
-euler_gamma
sage: psi(1)
-euler_gamma
# analytical result
sage: psi(1/2)
-euler_gamma - 2*log(2)
# numerical examples
sage: psi(.5)
-1.96351002602142
sage: psi(.5r)
-1.9635100260214233
sage: psi(complex(.5))
(-1.9635100260214233+0j)
# 1st argument means 0'th derivative (so psi(0, x) = psi(x))
sage: psi(0, .5)
psi(0.500000000000000)
sage: N(psi(0, .5))
-1.96351002602142
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6961#comment:8>
Sage <http://www.sagemath.org>
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