Let generalized hypergeometric
function
![_pF_q[alpha_1,alpha_2,...,alpha_p; beta_1,beta_2,...,beta_q;z]](/images/equations/Nearly-Poised/NumberedEquation1.svg) |
(1)
|
have 
.
Then the generalized hypergeometric function is said to be nearly-poised of the first
kind if
 |
(2)
|
(omitting the initial equality in the definition for well-poised),
and nearly-poised of the second kind if
 |
(3)
|
See also
Generalized Hypergeometric
Function,
k-Balanced,
Saalschützian
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References
Bailey, W. N. Generalised Hypergeometric Series. Cambridge, England: Cambridge University Press, pp. 11-12,
1935.Koepf, W. Hypergeometric
Summation: An Algorithmic Approach to Summation and Special Function Identities.
Braunschweig, Germany: Vieweg, p. 43, 1998.Whipple, F. J. W.
"On Well-Poised Series, Generalized Hypergeometric Series Having Parameters
in Pairs, Each Pair with the Same Sum." Proc. London Math. Soc. 24,
247-263, 1926.Referenced on Wolfram|Alpha
Nearly-Poised
Cite this as:
Weisstein, Eric W. "Nearly-Poised." From
MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Nearly-Poised.html
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