Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (3): 607-622.doi: 10.1016/S0252-9602(17)30026-7

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REFINEMENTS OF TRANSFORMATION INEQUALITIES FOR ZERO-BALANCED HYPERGEOMETRIC FUNCTIONS

Miaokun WANG, Yuming CHU   

  1. Department of Mathematics, Huzhou University, Huzhou 313000, China
  • Received:2015-07-07 Revised:2016-06-17 Online:2017-06-25 Published:2017-06-25
  • Supported by:
    This research was supported by the Natural Science Foundation of China (61673169,11401191,11371125),the Tianyuan Special Funds of the Natural Science Foundation of China (11626101),and the Natural Science Foundation of the Department of Education of Zhejiang Province (201635325).

Abstract: In the article, we present some refinements of three classes of transformation inequalities for zero-balanced hypergeometric functions by use of the updated monotonicity criterion for the quotient of power series.

Key words: Gauss hypergeometric function, complete elliptic integrals, quadratic transformation, Ramanujan cubic transformation

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