FW: a special 3_F_2

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

-----Original Message-----
From: opsftalk@nist.gov [mailto:opsftalk@nist.gov]On Behalf Of Irine
Peng
Sent: Tuesday, March 27, 2001 10:01 PM
To: dlozier@nist.gov
Subject: a speical 3_F_2


Sender: "Irine Peng" <irine_c_p@hotmail.com>
Subject: a speical 3_F_2


Hi,

I have a 3_F_2 sum that I want to show it is non-zero.

Specifically, a finite sum of the type:
3_F_2(-b2,b1+1,b1+1;b1+1-n,b1+2+n;1), where b1,b2,n are all positive
integers, with b1>n, seems to be non-zero for b1 not equal to b2, and I
want
to prove this.

For b2=b1+1, b2=b1-1, the sum is nearly-poised, and there are formulae
that
tell me the sum is non-zero. But I suspect there is no closed form
formulae
for this sum for arbitrary b2, and in order to show that it's non-zero
one
probably needs to use something else.

This sum comes from applying (del/delx - del/dely)^n to a family of
bivariate Jacobi polynomials written in Lauricella functions, followed
by
setting x=y=0.

Any help or suggestions would be greatly appreciated,

thank you,

Irine Peng
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