Replace the coefficient of abs in the lookup table of meijerint. #11283
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The denominator of the coefficient
pi/(cos(pi*a/2)*gamma(a))
becomes indeterminate for negative odd integers
a
wherecos(pi*a/2)
has a zero and
gamma(a)
has a pole. There is no code for computingthe limit at such argument values. This PR replaces the coefficient
with
2*sin(pi*a/2)*gamma(1 - a)
, which is well defined forre(a) < 1
,since the only poles of gamma occur at nonpositive integers.
The equivalence of the two forms can be derived from the standard
formulas
and