On values of hypergeometric functions with different irrational parameters

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