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Zbl 0619.33002
Bühring, Wolfgang
The behavior at unit argument of the hypergeometric function$ \sb 3F\sb 2$. (English)
[J] SIAM J. Math. Anal. 18, 1227-1234 (1987). ISSN 0036-1410; ISSN 1095-7154/e

The behavior at $z=1$ of the generalized hypergeometric function ${}\sb 3F\sb 2(a,b,c;e,f;z)$ is investigated. First the analytic continuation near $z=1$ is obtained for the general case when $s=e+f-a-b-c$ is not equal to an integer. The corresponding continuation formulas for the special cases when s is equal to an integer are then derived by appropriate limiting processes. When $f=c$ or $e=c$, the formulas immediately reduce to the well-known continuation formulas of the Gaussian hypergeometric function.

MSC 2000:: *33C05 Classical hypergeometric functions
34A30 Linear ODE and systems
34M99 Differential equations in the complex domain
30B40 Analytic continuation (one complex variable)

Keywords: hypergeometric differential equations

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