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The behavior at unit argument of the hypergeometric function 3 F 2 . (English) Zbl 0619.33002
The behavior at z=1 of the generalized hypergeometric function 3 F 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.
33C05Classical hypergeometric functions, 2 F 1
34A30Linear ODE and systems, general
34M99Differential equations in the complex domain
30B40Analytic continuation (one complex variable)