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.
Miaokun WANG
,
Yuming CHU
. REFINEMENTS OF TRANSFORMATION INEQUALITIES FOR ZERO-BALANCED HYPERGEOMETRIC FUNCTIONS[J]. Acta mathematica scientia, Series B, 2017
, 37(3)
: 607
-622
.
DOI: 10.1016/S0252-9602(17)30026-7
[1] Abramowitz M, Stegun I A. Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. Washington:US Government Printing Office, 1964
[2] Askey R. Handbooks of special functions//Duren P. A Century of Mathematcis in America. Part Ⅲ. Providence RI:Amer Math Soc, 1989:369-391
[3] Carlson B C. Special Functions of Applied Mathematics. New York:Academic Press, 1977
[4] Anderson G D, Vamanamurthy M K, Vuorinen M. Conformal Invariants, Inequalities, and Quasiconformal Maps. New York:John Wiley & Sons, 1997
[5] Berndt B C. Ramanujan's Notebooks. Part Ⅱ. New York:Springer-Verlag, 1989
[6] Anderson G D, Barnard R W, Richards K C, et al. Inequalities for zero-balanced hypergeometric functions. Trans Amer Math Soc, 1995, 347(5):1713-1723
[7] Anderson G D, Qiu S L, Vamanamurthy M K, et al. Generalized elliptic integrals and modular equations. Pacific J Math, 2000, 192(1):1-37
[8] Barnard R W, Pearce K, Richards K C. A monotonicity property involving 3F2 and comparisons of the classical approximations of elliptical arc length. SIAM J Math Anal, 2000, 32(2):403-419
[9] Berndt B C. Ramanujan's Notebooks. Part I. New York:Springer-Verlag, 1985
[10] Borwein J M, Borwein P B. Pi and the AGM. New York:John Wiley & Sons, 1987
[11] Olver F W J, Lozier D W, Boisvert R F, et al. NIST Handbook of Mathematical Functions. Cambridge:Cambridge University Press, 2010
[12] Qiu S L, Vuorinen M. Infinite products and normalized quotients of hypergeometric functions. SIAM J Math Anal, 1999, 30(5):1057-1075
[13] Whittaker E T, Watson G N. A Course of Modern Analysis. New York:Cambridge University Press, 1962
[14] Qiu S L, Vuorinen M. Special functions in geometric function theory//Kühnau R. Handbook of Complex Analysis:Geometric Function Theory. Vol 2. Amsterdam:Elsevier Science B V, 2005:621-659
[15] Qiu S L, Vuorinen M. Landen inequalities for hypergeometric functions. Nagoya Math J, 1999, 154:31-56
[16] Simić S, Vuorinen M. Landen inequalities for zero-balanced hypergeometric functions. Abstr Appl Anal, 2012, 2012, Article ID 932061, 11 pages
[17] Wang M K, Chu Y M, Jiang Y P. Ramanujan's cubic transformation inequalities for zero-balanced hypergeometric functions. Rocky Mountain J Math, 2016, 46(2):679-691
[18] Wang M K, Chu Y M, Jiang Y P, et al. A class of quadratic transformation inequalities for zero-balanced hypergeometric functions. Acta Math Sci, 2014, 34A(4):999-1007(in Chinese)
[19] Wang M K, Song Y Q, Chu Y M. Inequalities for zero-balanced hypergeometric functions. Acta Math Sinica, 2014, 57(4):719-726(in Chinese)
[20] 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
