Applied and computational complex analysis. Vol. 3: discrete Fourier analysis—Cauchy integrals—construction of conformal maps---univalent functions
Families of two-point Pade´ approximants and some 4F3(1) identities
SIAM Journal on Mathematical Analysis
N-point Padé approximants and two-sided estimates of errors on the real axis for Stieltjes functions
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the seventh international symposium on Orthogonal polynomials, special functions and applications
Asymptotic approximations for the first incomplete elliptic integral near logarithmic singularity
Journal of Computational and Applied Mathematics
Handbook of Continued Fractions for Special Functions
Handbook of Continued Fractions for Special Functions
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We find two-sided inequalities for the generalized hypergeometric function of the form "q"+"1F"q(-x) with positive parameters restricted by certain additional conditions. Both lower and upper bounds agree with the value of "q"+"1F"q(-x) at the endpoints of positive semi-axis and are asymptotically precise at one of the endpoints. The inequalities are derived from a theorem asserting the monotony of the quotient of two generalized hypergeometric functions with shifted parameters. The proofs hinge on a generalized Stieltjes representation of the generalized hypergeometric function. This representation also provides yet another method to deduce the second Thomae relation for "3F"2(1) and leads to an integral representations of "4F"3(x) in terms of the Appell function F"3. In the last section of the paper we list some open questions and conjectures.