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This article is cited in 1 scientific paper (total in 1 paper)
BRIEF MESSAGE
Values of hypergeometric F-series at polyadic Liouvillea points
E. Yu. Yudenkovaab a Russian Presidential Academy of National Economy and Public Administration (Moscow)
b Moscow Pedagogical State University (Moscow)
Abstract:
This paper proves infinite algebraic independence of the values of hypergeometric F – series at polyadic Liouville points. Hypergeometric functions are defined for |z|<1 by the power series: ∞∑n=0(α1)n⋯(αr)n(β1)n…(βs)nn!zn. F – series have form fn=∑∞n=0ann!zn whose coefficients an satisfy some arithmetic properties. These series converge in the field Qp of p – adic numbers and their algebraic extensions Kv. Polyadic number is a series of the form ∑∞n=0ann!,an∈Z. Liouville number is a real number x with the property that, for every positive integer n, there exist infinitely many pairs of integers (p,q) with q>1 such that 0<|x−pq|<1qn. The polyadic Liouville number α has the property that for any numbers P,D there exists an integer |A| such that for all primes p≤P the inequality |α−A|p<A−D.
Keywords:
hypergeometric F-series, polyadic Liouville numbers.
Citation:
E. Yu. Yudenkova, “Values of hypergeometric F-series at polyadic Liouvillea points”, Chebyshevskii Sb., 22:2 (2021), 536–542
Linking options:
https://www.mathnet.ru/eng/cheb1053 https://www.mathnet.ru/eng/cheb/v22/i2/p536
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Abstract page: | 97 | Full-text PDF : | 32 | References: | 19 |
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