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  4. The algorithms of constructing the continued fractions for any rations of the hypergeometric Gaussian functions

The algorithms of constructing the continued fractions for any rations of the hypergeometric Gaussian functions

MMC.
2017;
Volume 4, Number 1
: pp. 48-58
https://doi.org/10.23939/mmc2017.01.048
Received: June 15, 2017

Math. Model. Comput. Vol.4, No.1, pp.48-58 (2017)

Authors:
  1. Oleksandra Manziy
  2. Volodymyr Hladun
  3. L. Ventyk
1
Lviv Polytechnic National University
2
Lviv Polytechnic National University
3
Lviv Polytechnic National University

An algorithm for constructing recurrence relations of geometric Gaussian functions, in which the displacement of parameters is equal to $0$, $1$ or $-1$, is described. On the basis of such recurrence relations, the expansion for the ratio of Gaussian functions into continued fractions is developed. The obtained continued fractions are the development of the corresponding hypergeometric Gaussian functions in the case when the parameters of the function are integers.

Gaussian hypergeometric series
hypergeometric function
continued fraction
recurrence relation
expansion
ratio
algorithm
approximant
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