#14896: Implement symbolic confluent hypergeometric functions
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Reporter: eviatarbach | Owner: burcin
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.3
Component: symbolics | Resolution:
Keywords: hypergeometric | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/rws/ticket/14896 | b87c57b409b7d9df972ec88b7f0500e3ce51c89e
Dependencies: #2516 | Stopgaps:
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Comment (by nbruin):
If maxima can produce `gamma_greek` spontaneously, then we should be able
to make sense of it. The most straightforward way is by having a
transliteration, `gamma_incomplete_lower` or `gamma_lower` perhaps. Adding
new symbolic functions isn't ''that'' laborious, is it? Simplification
methods can be grown later.
FYI: Mathematica seems to have Gamma[a,z] for upper and Gamma[a,0,z] for
lower; Maple seems to have upper Gamma. So it does seem packages have been
gravitating to the upper one more than the lower one. However, if that
means our confluent hypergeometric functions always end up being
translated into a more convoluted expression than a straight gamma_lower
would give, we're not doing ourselves favours
(e.g., for numerical work: do you really want to evaluate gamma_lower(a,z)
as gamma(z)-gamma_upper(a,z) ?)
Without strong indications in either direction, I'd be hesitant to make a
choice and rather follow the lead of our main underlying engine: implement
gamma_lower.
--
Ticket URL: <http://trac.sagemath.org/ticket/14896#comment:18>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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