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Recurrence relations for hypergeometric functions of unit argument. (English) Zbl 0583.33005

The author shows that the generalized hypergeometric function

P n := p+3 F p+2 -n,n+λ,a p ,1;1b p+2 ,n0

satisfies a nonhomogeneous recurrence relation of order p, when p+3 F p+2 (1) is balanced, and of order p+1 otherwise. For

U n :=((c q+1 ) n /(d q ) n (n+λ) n ) q+2 F q+1 n+c q+2 ;1n+d q ,2n+λ+1,n0

a homogeneous recurrence relation of order q+1 is given. The results are proved by using some general theorems due to J. Wimp [Math. Comput. 22, 363-373 (1968; Zbl 0186.104); ibid. 29, 577-581 (1975; Zbl 0304.33003)] and Y. Luke [The special functions and their approximations (1969; Zbl 0193.017)]. Some examples are given.

Reviewer: S.L.Kalla

MSC:
33C05Classical hypergeometric functions, 2 F 1
65D20Computation of special functions, construction of tables
65Q05Numerical methods for functional equations (MSC2000)