## Approximation of hypergeometric functions with matricial argument through their development in series of zonal polynomials

R. Gutiérrez, J. Rodriguez and A. J. Sáez

### Abstract

Hypergeometric functions with matricial argument are being used in several fields of mathematics. This article tries to obtain a good approximation of this family of functions, since there are no general expressions for them, calculating zonal polynomials of high degrees and developing the functions in a truncated series.

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### Key words

hypergeometric functions with matricial argument, zonal polynomials.

### AMS subject classifications

33C20, 33C99, 12Y05.

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