Two double inequalities for k-gamma and k-Riemann zeta functions

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• 作者：Jing Zhang (17)
  Huan-Nan Shi (18)
  
  17. Basic Courses Department ; Beijing Union University ; Beijing ; 100101 ; P.R. China
  18. Department of Electronic Information ; Teacher鈥檚 College ; Beijing Union University ; Beijing ; 100011 ; P.R. China
  
• 关键词：majorization ; Schur convexity ; k ; gamma function ; k ; Riemann zeta function ; Ap茅ry鈥檚 constant ; log ; convexity
• 刊名：Journal of Inequalities and Applications
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：2014
• 期：1
• 全文大小：165 KB
• 参考文献：1. Andrews, GE, Askey, R, Roy, R (1999) Special Functions. Cambridge University Press, Cambridge CrossRef
  2. Alsina C, Tom谩s MS: A geometrical proof of a new inequality for the gamma function. / J. Inequal. Pure Appl. Math. 2005.,6(2): Article ID 48
  3. Nguyen, VV, Ngo, PNN (2009) An inequality for the gamma function. Int. Math. Forum 4: pp. 1379-1382
  4. D铆az, R, Pariguan, E (2007) On hypergeometric functions and Pochhammer k-symbol. Divulg. Mat 15: pp. 179-192
  5. Kokologiannaki, CG, Krasniqi, V (2013) Some properties of the k-gamma function. Matematiche 68: pp. 13-22
  6. D铆az, R, Teruel, C (2005) -Generalized gamma and beta functions. J. Nonlinear Math. Phys 12: pp. 118-134 CrossRef
  7. van der Poorten, A (1979) A proof that Euler missed. Math. Intell 1: pp. 195-203 CrossRef
  8. Marshall, AW, Olkin, I, Arnold, BC (2011) Inequalities: Theory of Majorization and Its Application. Springer, New York
  9. Wang, BY (1990) Foundations of Majorization Inequalities. Beijing Normal University Press, Beijing
  10. Hardy, GH, Littlewood, JE, P贸lya, G (1934) Inequalities. Cambridge University Press, London
  11. Marshall, AW, Olkin, I (2009) Schur-convexity, gamma functions, and moments. Int. Ser. Numer. Math 157: pp. 245-250
  12. Merkle, M (1997) On log-convexity of a ratio of gamma functions. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat 8: pp. 114-119
  13. Merkle, M (1998) Conditions for convexity of a derivative and some applications to the gamma function. Aequ. Math 55: pp. 273-280 CrossRef
  
• 刊物主题：Analysis; Applications of Mathematics; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1029-242X

文摘

By using methods in the theory of majorization, a double inequality for the gamma function is extended to the k-gamma function and the k-Riemann zeta function. MSC: 33B15, 26D07, 26B25.