[1] Qureshi M I, Akhtar N, Ahamad D. Analytical expressions for curved surface area of revolution and arclength of an ellipse:A hypergeometric mechanism. Trans Natl Acad Sci Azerb Ser Phys-Tech Math Sci Mathematics, 2020, 40(1):152-160
[2] Zhao T H, He Z Y, Chu Y M. On some refinements for inequalities involving zero-balanced hypergeometric function. AIMS Math, 2020, 5(6):6479-6495
[3] Zhao T H, Wang M K, Chu Y M. Concavity and bounds involving generalized ellipic integral of the first kidn. J Math Inequal, 2021, 15(2):701-724
[4] Wang M K, Chu H H, Chu Y M. On the approximation of some special functions in Ramanujan's generalized modular equation with signature 3. Ramanujan J, 2021, 56(1):1-22
[5] Zhao T H, Shi L, Chu Y M. Convexity and concavity of the modified Bessel functions of the first kind with respect to Hölder means. Rev R Acad Cienc Exactas Fís Nat Ser A Mat RACSAM, 2020, 114(2):Article 96
[6] Yang Z H, Qian W M, Chu Y M, Zhang W. On rational bounds for the gamma function. J Inequal Appl, 2017, 2017:Article ID 210
[7] Chu Y M, Zhao T H. Concavity of the error function with respect to Hölder means. Math Inequal Appl, 2016, 19(2):589-595
[8] Zhao T H, Qian W M, Chu Y M.:On approximating the arc lemniscate functions. Indian J Pure Appl Math, 2021. https://doi.org/10.1007/s13226-021-00016-9
[9] Li L, Wang W K, Huang L H, Wu J. Some weak flocking models and its application to target tracking. J Math Anal Appl, 2019, 480(2):Article ID 123404
[10] Zhao T H, Bhayo B A, Chu Y M. Inequalities for generalized Grötzsch ring funciton. Comput Methods Funct Theory, 2021. https://doi.org/10.1007/s40315-021-00415-3
[11] Anderson G D, Qiu S L, Vuorinen M. Precise estimates for differences of the Gaussian hypergeometric function. J Math Anal Appl, 1997, 215(1):212-234
[12] Xu H Z, Qian W M, Chu Y M. Sharp bounds for the lemniscatic mean by the one-parameter geometric and quadratic means. Rev R Acad Cienc Exactas Fís Nat Ser A Mat RACSAM, 2022, 116(1):Article 21
[13] Anderson G D, Vamanamurthy M K, Vourinen M. Conformal Invariants, Inequalities, and Quasiconformal Maps. New York:John wiley & Sons, 1997
[14] Chu H H, Zhao T H, Chu Y M. Sharp bounds for the Toadr mean of order 3 in tems of arithmetic, quadratic and contraharmonic means. Math Slovaca, 2020, 70(5), 1097-1112
[15] Zhao T H, Zhou B C, Wang M K, Chu Y M. On approximating the quasi-arithmetic means. J Inequal Appl, 2019, 2019:Article 42
[16] Zhao T H, Shen Z H, Chu Y M. Sharp power mean bounds for the lemniscate type means. Rev R Acad Cienc Exactas Fís Nat Ser A Mat RACSAM, 2021, 115(4):Article 175
[17] Wang M K, Chu Y M, Song Y Q. Asymptotical formulas for Gaussian and generalized hypergeometric functions. Appl Math Comput, 2016, 276:44-60
[18] 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
[19] Wang M K, Chu Y M. Refinements of transformation inequalities for zero-balanced hypergeometric functions. Acta Math Sci, 2017, 37B(3):607-622
[20] Wang M K, Chu Y M. Landen inequalities for a class of hypergeometric functions with applications. Math Inequal Appl, 2018, 21(2):521-537
[21] Zhao T H, Wang M K, Hai G J, Chu Y M. Landen inequalities for Gaussian hypergeometric function. Rev R Acad Cienc Exactas Fís Nat Ser A Mat RACSAM, 2021. https://doi.org/10.1007/s13398-021-01197-y
[22] Wang M K, Chu Y M, Zhang W. Monotonicity and inequalities involving zero-balanced hypergeometric function. Math Inequal Appl, 2019, 22(2):601-617
[23] Zhao T H, Wang M K, Zhang W, Chu Y M. Quadratic transformation inequalities for Gaussian hypergeometric function. J Inequal Appl, 2018, 2018:Article 251
[24] Zhou S S, Rashid S, Noor M A, et al. New Hermite-Hadamard type inequalities for exponentially convex functions and applications. AIMS Math, 2020, 5(6):6874-6901
[25] Li Y X, Rauf A, Naeem M, et al. Valency-based topological properties of linear hexagonal chain and hammer-like benzenoid. Complexity, 2021, 2021:Article ID 9939469
[26] Chen S B, Rashid S, Noor M A, et al. A new approach on fractional calculus and probability density function. AIMS Math, 2020, 5(6):7041-7054
[27] Chen S B, Jahanshahi H, Alhadji Abba O, et al. The effect of market confidence on a financial system from the perspective of fractional calculus:numerical investigation and circuit realization. Chaos Solitons Fractals, 2020, 140:Article ID 110223
[28] Chu Y M, Wang M K. Optimal Lehmer mean bounds for the Toader mean. Results Math, 2012, 61:223-229
[29] Yang Z H, Chu Y M, Zhang W. High accuracy asymptotic bounds for the complete elliptic integral of the second kind. Appl Math Comput, 2019, 348:552-564
[30] Yang Z H, Qian W M, Chu Y M, Zhang W. On approximating the arithmetic-geometric mean and complete elliptic integral of the first kind. J Math Anal Appl, 2018, 462(2):1714-1726
[31] Yang Z H. Sharp approximations for the complete elliptic integrals of the second kind by one-parameter means. J Math Anal Appl, 2018, 467:446-461
[32] Yang Y Y, Qian W M, Zhang H W, Chu Y M. Sharp bounds for Toader-type means in terms of twoparameter means, Acta Math Sci, 2021, 41B(3):719-728
[33] Wang M K, Chu Y M. Refinements of transformation inequalities for zero-balanced hypergeometric functions. Acta Math Sci, 2017, 37B(3):607-622
[34] Qiu S L, Ma X Y, Chu Y M. Extensions of quadratic transformation identities for hypergeometric functions. Math Inequal Appl, 2020, 23(4):1391-1423
[35] Zhao T H, He Z Y, Chu Y M. On some refinements for inequalities involving zero-balanced hypergeometric function. AIMS Math, 2020, 5(6):6479-6495
[36] Qiu S L, Ma X Y, Chu Y M. Sharp Landen transformation inequalities for hypergeometric functions, with applications. J Math Anal Appl, 2019, 474(2):1306-1337
[37] Qian W M, Wang M K, Xu H Z, Chu Y M. Approximations for the complete elliptic integral of the second Kind. Rev R Acad Cienc Exactas Fís Nat Ser A Mat RACSAM, 2021, 115(2):Article 88
[38] Zhao T H, Wang M K, Chu Y M. Monotonicity and convexity involving generalized elliptic integral of the first kind. Rev R Acad Cienc Exactas Fíis Nat Ser A Mat RACSAM, 2021, 115(2):Article 46
[39] Huang X F, Wang M K, Shao H, et al. Monotonicity properties and bounds for the complete p-elliptic integrals. AIMS Math, 2020, 5(6):7071-7086
[40] Zhao T H, Wang M K, Chu Y M. A sharp double inequality involving generalized complete elliptic integral of the first kind. AIMS Math, 2020, 5(5):4512-4528
[41] Wang M K, Chu Y M, Li Y M, Zhang W. Asymptotic expansion and bounds for complete elliptic integrals. Math Inequal Appl, 2020, 23(3):821-841
[42] Wang M K, Chu H H, Li Y M, Chu Y M. Answers to three conjectures on convexity of three functions involving complete elliptic integrals of the first kind. Appl Anal Discrete Math, 2020, 14(1):255-271
[43] Wang M K, He Z Y, Chu Y M. Sharp power mean inequalities for the generalized elliptic integral of the first kind. Comput Methods Funct Theory, 2020, 20(1):111-124
[44] Zhao T H, He Z Y, Chu Y M. Sharp bounds for weighted Hölder mean of the zero-balanced generalized complete elliptic integrals. Comput Methods Funct Theory, 2021, 21(3):413-426
[45] Yang Z H, Qian W M, Zhang W, Chu Y M. Notes on the complete elliptic integral of the first kind. Math Inequal Appl, 2020, 23(1):77-93
[46] Qian W M, He Z Y, Chu Y M. Approximation for the complete elliptic integral of the first kind. Rev R Acad Cienc Exactas Fís Nat Ser A Mat RACSAM, 2020, 114(2):Article 57
[47] Wang M K, Chu H H, Chu Y M. Precise bounds for the weighted Hölder mean of the complete p-elliptic integrals. J Math Anal Appl, 2019, 480(2):Article ID 123388
[48] Wayne A. A table for computing perimeters of ellipses. Amer Math Monthly, 1944, 51:219-220
[49] Frucht R. On the numerical calculation of the perimeter of an ellipse. Math Notae, 1947, 7:212-217
[50] Gupta R C. Mahāvīrācarya on the perimeter and area of an ellipse. Math Education, 1974, 8:B17-B19
[51] Barnard R W, Pearce K, Schovanec L. Inequalities for the perimeter of an ellipse. J Math Anal Appl, 2001, 260(2):295-306
[52] Villarino M B. A note on the accuracy of Ramanujan's approximative formula for the perimeter of an ellipse. JIPAM J Inequal Pure Appl Math, 2006, 7(1):Article 21
[53] Chandrupatla T R, Thomas J. The perimeter of an ellipse. Math Sci, 2010, 35(2):122-131
[54] Adlaj S. An eloquent formula for the perimeter of an ellipse. Notices Amer Math Soc, 2012, 59(8):1094- 1099
[55] Gusić I. On the bounds for the perimeter of an ellipse. Math Gaz, 2015, 99(546):540-541
[56] Hemati S, Beiranvand P, Sharafi M. Ellipse perimeter estimation using non-parametric regression of RBF neural network based on elliptic integral of the second type. Investigación Oper, 2018, 39(4):639-646
[57] Vuorinen M. Hypergeometric functions in geometric function theory//Special Functions and Differential Equations. Madras, 1997:119-126; New Delhi:Allied Publ, 1998
[58] Barnard R W, Pearce K, Richards K C. An inequality involving the generalized hypergeometric function and the arc length of an ellipse. SIAM J Math Anal, 2000, 31(3):693-699
[59] Alzer H, Qiu S L. Monotonicity theorems and inequalities for the complete elliptic integrals. J Comput Appl Math, 2004, 172(2):289-312
[60] Wang M K, Chu Y M, Qiu S L, Jiang Y P. Bounds for the perimeter of an ellipse. J Approx Theory, 2012, 164(7):928-937
[61] Wang M K, Chu Y M, Jiang Y P, Qiu S L. Bounds of the perimeter of an ellipse using arithmetic, geometric and harmonic means. Math Inequal Appl, 2014, 17(1):101-111
[62] He Z Y, Wang M K, Jiang Y P, Chu Y M. Bounds for the perimeter of an ellipse in terms of power means. J Math Inequal, 2020, 14(3):887-899
[63] Yang Z H, Chu Y M. Inequalities for certain means in two arguments. J Inequal Appl, 2015, 2015:Article 299
[64] Qi F. Bounds for the ratio of two gamma functions. J Inequal Appl, 2010, 2010:Article ID 493058
