Acta mathematica scientia,Series A ›› 2018, Vol. 38 ›› Issue (1): 46-53.
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Yin Li, Huang Liguo
Received:
2016-07-10
Revised:
2017-05-20
Online:
2018-02-26
Published:
2018-02-26
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CLC Number:
Yin Li, Huang Liguo. Two Inequalities Related to Generalized Elliptic Integrals[J].Acta mathematica scientia,Series A, 2018, 38(1): 46-53.
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[1] Abramowitz M, Stegun I A. Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. Washington:US Government Printing Office, 1964 [2] Andrews G E, Askey R, Roy R. Special Functions. Cambridge:Cambridge University Press, 1999 [3] Wang M K, Chu Y M. Refinements of transformation inequalities for zero-balanced hypergeometric functions. Acta Math Sci, 2017, 37B(3):607-622 [4] Wang M K, Li Y M, Chu Y M. Inequalities and infinite product formula for Ramanujan generalized modular equation function. Ramanujan J, 2017, 43:1-12 [5] Yang Z H, Chu Y M, Zhang X H. Sharp stolarsky mean bounds for the complete elliptic integral of the second kind. J Nonlinear Sci Appl, 2017, 10(3):929-936 [6] Yang Z H, Chu Y M, Zhang W. Accurate approximations for the complete elliptic integral of the second kind. J Math Anal Appl, 2016, 438(2):875-888 [7] Yang Z H, Chu Y M, Wang M K. Monotonicity criterion for the quotient of power series with applications. J Math Anal Appl, 2015, 428(1):587-604 [8] Wang M K, Chu Y M. Asymptotical bounds for complete elliptic integrals of the second kind. J Math Anal Appl, 2013, 402(1):119-126 [9] 王淼坤, 褚玉明, 蒋月评, 闫丹丹. 零平衡超几何函数的一类二次变换不等式. 数学物理学报, 2014, 34A(4):999-1007 Wang M K, Chu Y M, Jiang Y P, Yan D D. A class of quadtrtic transformation inequalities for zero-balanced hypergeometric functions. Acta Math Sci, 2014, 34A(4):999-1007 [10] Ma X Y, Chu Y M, Wang F. Monotonicity and inequalities for the generalized distortion function. Acta Math Sci, 2013, 33B(6):1759-1766 [11] 王根娣, 张孝惠, 褚玉明, 裘松良. 完全椭圆积分和Hersch-Pfluger偏差函数. 数学物理学报, 2008, 28A(4):731-734 Wang G D, Zhang X H, Chu Y M, Qiu S L. Complete elliptic integrals and the Hersch-Pfluger distortion function. Acta Math Sci, 2008, 28A(4):731-734 [12] 张孝惠, 裘松良, 褚玉明, 王根娣. 广义Grötzsch环函数的几个精确不等式. 数学物理学报, 2008, 28A(1):59-65 Zhang X H, Qiu S L, Chu Y M, Wang G D. Some sharp inequalities for a generalized Grötzsch ring function. Acta Math Sci, 2008, 28A(1):59-65 [13] Alzer H, Qiu S L. Monotonicity theorems and inequalities for the generalized complete elliptic integrals. J Comput Appl Math, 2004, 172(2):289-312 [14] Alzer H, Richards K. A note on a function involving complete elliptic integrals:monotonicity, convexity, inequalities. Anal Math, 2015, 41(3):133-139 [15] Heikkala V, Vamanamurthy M K, Vuorinen M. Generalized elliptic integrals. Comput Methods Funct Theory, 2009, 9(1):75-109 [16] Lindqvist P. Some remarkable sine and cosine functions. Ricerche Mat, 1995, 44(2):269-290 [17] Jiang W D, Wang M K, Chu Y M, Jiang Y P, Qi F. Convexity of the generalized sine function and the generalized hyperbolic sine function. J Approx Theory, 2013, 174:1-9 [18] Song Y Q, Chu Y M, Liu B Y, Wang M K. A note on generalized trigonometric and hyperbolic functions. J Math Inequal, 2014, 8(3):635-542 [19] Drábek P, Manásevich R. On the closed solution to some nonhomogeneous eigenvalue problems with p-Laplacian. Differential Integrals Equations, 1999, 12(6):773-788 [20] Takeuchi S. A new form of the generalized complete elliptic integrals. Kodai Math J, 2016, 39(1):202-226 [21] Wang M K, Chu Y M, Song Y Q. Asymptotical formulas for Gaussian and generalized hypergeometric functions. Appl Math Comput, 2016, 276:44-60 [22] Wang M K, Chu Y M, Qiu S L. Sharp bounds for generalized elliptic integrals of the first kind. J Math Anal Appl, 2015, 429(2):744-757 [23] Zhang X H, Wang G D, Chu Y M. Remarks on generalized elliptic integrals. Proc Roy Soc Edinburgh Sect A, 2009, 139(2):417-426 [24] Wang G D, Zhang X H, Chu Y M. Inequalities for the generalized elliptic integrals and modular functions. J Math Anal Appl, 2007, 331(2):1275-1283 [25] Wang M K, Qiu S L, Chu Y M, Jiang Y P. Generalized Hersch-Pfluger distortion function and complete elliptic integrals. J Math Anal Appl, 2012, 385(1):221-229 [26] Prudnikov A P, Brychkov Y A, Marichev O I. Integrals and Series (Volume 3):More Sepcial Functions. New York:Gordon and Breach Science Publishers, 1990 [27] Wang Z X, Guo D R. Special Functions. Teaneck:World Scientific Publishing Co, 1989 |
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