FW: Matrix of potentials in Legendre basis

["Daniel Lozier" <lozier@nist.gov>]

George: Thanks for the reply, which I am resending to the mailing list.

Dan Lozier

-----Original Message-----
From: George Gasper [mailto:george@math.northwestern.edu]
Sent: Monday, February 12, 2001 3:53 PM
To: dlozier@nist.gov
Cc: george@poincare.math.nwu.edu
Subject: FW: Matrix of potentials in Legendre basis


Dan,

The summational formula in your email message of Frb. 12th:

3. (Some hypergeometric summation formula)
$$
   _3 F_2(a, 1-a, (b+c-1)/2;
          b,c;
             1)=
   2^{2-b-c} \pi
   \frac{\Gamma(b)\Gamma(c)}%
        {\Gamma((b+a)/2) \Gamma((b+a')/2)
         \Gamma((c+a)/2) \Gamma((c+a')/2)}
$$
 Here a'=1-a.
 The series is not balanced, well-poised or terminating.

is equivalent to Whipple's formula 4.4(7) in Erdelyi et al., vol 1. p.
189.

Best wishes,
George

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