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Nearly-Poised

A nearly-poised generalized hypergeometric function

_pF_q[alpha_1,alpha_2,...,alpha_p; beta_1,beta_2,...,beta_q;z]
(1)

satisfies p=q+1 and is of the first kind if

beta_1+alpha_2=...=beta_q+alpha_(q+1),
(2)

(omitting the initial equality in the definition for well-poised), and of the second kind if

1+alpha_1=beta_1+alpha_2=...=beta_(q-1)+alpha_q.
(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.

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Nearly-Poised

Cite this as:

Weisstein, Eric W. "Nearly-Poised." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Nearly-Poised.html

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