FW: Whipple's summation formula

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

Editor's Note:  See also "Matrix of potentials in Legendre basis"
group of messages in the opsftalk archive. - Dan Lozier

-----Original Message-----
From: opsftalk@nist.gov [mailto:opsftalk@nist.gov]On Behalf Of Sadov
Sent: Sunday, February 18, 2001 11:59 AM
To: dlozier@nist.gov
Subject: Whipple's summation formula

Sender: Sadov <sadov@spp.keldysh.ru>
Subject: Whipple's summation formula


I wish to thank Professors Gasper and Askey for
quick and informative answers. I also received
a letter in Russian from Prof. Krupnikov;
translation of a part of it follows below.
Of course, it was my big negligence to miss Whipple's
formula in Erdelyi's volume. I've read the proof in
Bailey's tract. My approach is quite different, though
by far not shorter if one considers Whipple's formula as
the final goal. I'll outline it in the next post.

I have yet to look into refs given by Prof.Askey.

Sergey Sadov

------
>From ernst@neic.nsk.su Tue Feb 13 17:46:06 2001
Date: Tue, 13 Feb 2001 15:20:11 +0530
From: Ernst Davidovich Krupnikov <ernst@neic.nsk.su>
To: sadov@keldysh.ru
Subject: the Whipple summation theorem

Regarding your third question. This is Whipple summation theorem
(F. J. W. Whipple, Proceedings of the London Mathematical Society,
1925, vol. 23, pages 104--114). See "Higher Transcendental functions"
sect.4.4, (7), also Yudell Luke "Special mathematical functions and
their approximations" (p.173 in Rus.translation [Mir,1980], (5)),
and A.P.Prudnikov, Yu.A.Brychkov, O.I.Marichev, "Integrals and Series:
Further results" [in Russian], Nauka, 1986, p.535, (24).
Whipple's paper is mentioned in classical monographs
by W. N. Bailey and L. J. Slater.

                     Ernst Davidovich Krupnikov