论文信息 - Numerically satisfactory solutions of hypergeometric recursions

Numerically satisfactory solutions of hypergeometric recursions

Each family of Gauss hypergeometric functions fn = 2F1(a + "1n, b + "2n; c + "3n; z), n ∈ Z , for fixed "j = 0, ±1 (not all "j equal to zero) satisfies a second order linear difference equation of the form Anfn 1 + Bnfn + Cnfn+1 = 0. Because of symmetry relations and functional relations for the Gauss functions, many of the 26 cases (for different "j values) can be transformed into each other. In this way, only with four basic difference equations all other cases can be obtained. For each of these recurrences, we give pairs of numerically satisfactory solutions in the regions in the complex plane where |t1| 6= |t2|, t1 and t2 being the roots of the characteristic equation.

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