A new approach was developed to the construction and
investigation of Pade approximants based on generalized
moment representations. In particular, the following results
were obtained:
convergence and asymptotics of diagonal Pade approximants for
functions of Mittag-Leffler type;
convergence of simultaneous Pade approximants for
systems of confluent hypergeometric functions and
systems of functions of Mittag-Leffler type;
exact formulae for Pade approximants for some
basic hypergeometric functions;
application of generalized moment representations
to the problem of Pade-Chebyshev approximation;
application of generalized moment representations
to multipoint Pade approximation;
generalization of invariance properties of Pade
approximants.
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E-mail: golub@imath.kiev.ua
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