E1867

Shafer, R. E.; Grinstein, Louise S.; Marsh, D. C. B.; Konhauser, J. D. E.

doi:10.2307/2314285

Cited by 9 publications

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“…The origins of these are to be found in [1] and [2] and a large bibliography concerning them and their extensions appears in [3]. Our purpose in this note is to generalize these results to the case in which sin θ is replaced by the Jacobi elliptic function sn(u|k) .…”

Section: Introductionmentioning

confidence: 93%

Shafer-Fink type inequalities for the elliptic function sn(u|k)

Mercer¹

2008

Journal of Mathematical Inequalities

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Section: Introductionmentioning

confidence: 93%

Shafer-Fink type inequalities for the elliptic function sn(u|k)

Mercer¹

2008

Journal of Mathematical Inequalities

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“…In 1966, Shafer [1] posed, as a problem, the following inequality: Three proofs of it were later given in [2]. Shafer’s inequality (1.1) was sharpened and generalized by Qi et al in [3].…”

Section: Introductionmentioning

confidence: 99%

Approximations to inverse tangent function

Qiao

Chen

2018

J Inequal Appl

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Topics in Special Functions III

Anderson

Вуоринен

Zhang

2014

Analytic Number Theory, Approximation Theory, and Special Functions

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The study of quasiconformal maps led the first two authors in their joint work with M. K. Vamanamurthy to formulate open problems or questions involving special functions [14,16]. During the past two decades, many authors have contributed to the solution of these problems. However, most of the problems posed in [14] are still open.The present paper is the third in a series of surveys by the first two authors, the previous papers [19,21] being written jointly with the late M. K. Vamanamurthy. The aim of this series of surveys is to review the results motivated by the problems in [14,16] and related developments during the past two decades. In the first of these we studied classical special functions, and in the next we focused on special functions occurring in the distortion theory of quasiconformal maps. Regretfully, Vamanamurthy passed away in 2009, and the remaining authors dedicate the present work as a tribute to his memory. For an update to the bibliographies of [19] and [21] the reader is referred to [23].In 1993 the following monotone rule was derived [17, Lemma 2.2]. Though simple to state and easy to prove by means of the Cauchy Mean Value Theorem, this l'Hôpital Monotone Rule (LMR) has had wide application to special functions by many authors. Vamanamurthy was especially skillful in the application of this rule. We here quote the rule as it was restated in [20, Theorem 2].

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E1867

Cited by 9 publications

References 0 publications

Shafer-Fink type inequalities for the elliptic function sn(u|k)

Shafer-Fink type inequalities for the elliptic function sn(u|k)

Approximations to inverse tangent function

Topics in Special Functions III

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