Acta mathematica scientia,Series A ›› 2020, Vol. 40 ›› Issue (3): 662-666.

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The Simple Proof and Generalization of a Conjecture Concerning Generalized Legendre Identity

Miaokun Wang1,*(),Yuming Chu1(),Songliang Qiu2()   

  1. 1 College of Science, Huzhou University, Zhejiang Huzhou 313000
    2 College of Science, Zhejiang Sci-Tech University, Hangzhou 310038
  • Received:2019-07-27 Online:2020-06-26 Published:2020-07-15
  • Contact: Miaokun Wang E-mail:wmk000@126.com;chuyuming@zjhu.edu.cn;sl_qiu@zstu.edu.cn
  • Supported by:
    the NSFC(11701176);the NSFC(61373169)

Abstract:

In this paper, some monotonicity properties of certain combinations of Gaussian hypergeometric function are proved, and using these properties, the simple proof and generalization of a conjecture about generalized Legendre identity are presented, which will be helpful to the study of special functions.

Key words: Gaussian hypergeometric functions, Legendre identity, Monotonicity, Convexity

CLC Number: 

  • O174.6
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