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On values of hypergeometric functions with different irrational parameters

Abstract

In this paper, we study the arithmetic nature of the values of generalized hypergeometric functions with different irrational parameters. Linear independence of such values is proved by means of an effective construction of the Pade approximation; corresponding quantitative results are obtained.

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Correspondence to P. L. Ivankov.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 6, pp. 65–72, 2005.

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Ivankov, P.L. On values of hypergeometric functions with different irrational parameters. J Math Sci 146, 5674–5679 (2007). https://doi.org/10.1007/s10958-007-0383-z

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Keywords

  • Hypergeometric Function
  • Common Denominator
  • Linear Independence
  • Arithmetic Property
  • Generalize Hypergeometric Function