[Maxima-bugs] [ maxima-Bugs-1376860 ] specint(gammaincomplete(v, a*t)*exp(-p*t), t) seems wrong

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Bugs item #1376860, was opened at 2005-12-08 20:53
Message generated for change (Settings changed) made by robert_dodier
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>Category: Lisp Core - Integration
Group: None
Status: Open
Resolution: None
Priority: 5
Submitted By: Raymond Toy (rtoy)
Assigned to: Nobody/Anonymous (nobody)
Summary: specint(gammaincomplete(v,a*t)*exp(-p*t),t) seems wrong

Initial Comment:
(%i12) assume(v>0,p>0);

(%o12) [v>0,p>0]
(%i13) specint(gammaincomplete(v,a*t)*exp(-p*t),t);

SIMP2F1-WILL-CONTINUE-IN 
(%o13)
a^v*(p+a)^(-v-1)*gamma(v+1)*%f[2,1]([v+1,3/2],[2],p/(p+a))

Compare this with

(%i14) specint(gammagreek(v,a*t)*exp(-p*t),t);
(%o14) a^v*p^(-v-1)*gamma(v+1)/((a/p+1)^v*v)

This matches formula 34, p 179 in Tables of Transforms.
Considering gammaincomplete = gamma(n)-gammagreek, the
expression for gammaincomplete seems wrong.  

It might still be right if the hypergeometric function
simplifies, but maxima can't, and I can't think of any
way to simplify it either.


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Comment By: Raymond Toy (rtoy)
Date: 2006-02-12 12:15

Message:
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The fix for transforming %w causes this return the result in
terms of the associated Legendre function Q.  Somewhat
better, but I do not know if this is equivalent.

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