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Well-Poised

A generalized hypergeometric function

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

is said to be well-poised if p=q+1 and

1+alpha_1=beta_1+a_2=...=beta_q+alpha_(q+1).

See also

Generalized Hypergeometric Function, k-Balanced, Nearly-Poised, Saalschützian

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References

Bailey, W. N. Generalised Hypergeometric Series. Cambridge, England: Cambridge University Press, p. 11, 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.Whipple, F. J. W. "Well-Poised Series and Other Generalized Hypergeometric Series." Proc. London Math. Soc. Ser. 2 25, 525-544, 1926.

Referenced on Wolfram|Alpha

Well-Poised

Cite this as:

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

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