Abstract
The general problem of Padé approximation to a system of functions satisfying linear differential equations is considered. We use the method of isomonodromy deformation to construct effectively the remainder function and Pade approximants in the case of N-point approximations of solutions of Fuchsian linear differential equations. Special attention is devoted to generalized hypergeometric functions gFp (a1,…,a2;b1,…,bp;x). In various cases the asymptotics of the remainder function is presented. A separate section is devoted to applications of analytic methods to the problem of rational and diophantine approximations of the values at rational and algebraic points of functions satisfying linear differential equations. There is presented also an analytic method for investigation of the arithmetic nature of the constants, arising as values of hypergeometric functions, such as L2 (1/q): q ≥14, ζ(2), ζ(3) etc.. which occur in many physical situations.
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Chudnovsky, G.V. (1980). Padé Approximation and the Riemann Monodromy Problem. In: Bardos, C., Bessis, D. (eds) Bifurcation Phenomena in Mathematical Physics and Related Topics. NATO Advanced Study Institutes Series, vol 54. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9004-3_21
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DOI: https://doi.org/10.1007/978-94-009-9004-3_21
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