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By Pietro Cerone

ISBN-10: 1600219195

ISBN-13: 9781600219191

This e-book is the 1st in a suite of analysis monographs which are dedicated to offering fresh study, improvement and use of Mathematical Inequalities for distinct capabilities. the entire papers integrated within the ebook have peen peer-reviewed and canopy more than a few themes that come with either survey fabric of formerly released works in addition to new effects. In his presentation on distinctive services approximations and boundaries through necessary illustration, Pietro Cerone utilises the classical Stevensen inequality and limits for the Ceby sev useful to procure bounds for a few classical detailed services. The technique is dependent upon deciding on bounds on integrals of goods of services. The suggestions are used to acquire novel and necessary bounds for the Bessel functionality of the 1st variety, the Beta functionality, the Zeta functionality and Mathieu sequence.

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It is clear that αn is increasing if b > 0 and decreasing if b < 0. Therefore, the sequences n1b , n1c are synchronous if bc ≥ 0 and asynchronous when bc < 0. 5) is proved. 2. 6) provided the real numbers a, b are such that a, a + b, a + 2b > 1. 3). 3. Assume that m ≥ 2 and k1, . . , km > 12 . 7) 1≤i

Math. , 13(1) (1982), 1–8. ¨ [33] O. E. Emersleben, Uber die Reihe ∞ k=1 k(k2 +c2 )−2 , Math. , 125 (1952), 165–171. R. Finch, Mathematical Constants, Cambridge Univ. Press, Cambridge, 2003. M. Fink, A treatise on Gr¨ uss’ inequality, Analytic and Geometric Inequalites and Applications, Math. , 478 (1999), Kluwer Academic Publishers, Dordrecht, 93114. [36] I. Gavrea, Some remarks on Mathieu’s series, Mathematical Analysis and Approximation Theory, 113-117, Burg Verlag, 2002. -N. Guo, Note on Mathieu’s inequality, RGMIA Res.

39] J. Havil, Gamma: Exploring Euler’s constant, Princeton University Press, New Jersey, 2003. [40] L. Landau, Monotonicity and bounds on Bessel functions, Electronic J. of Differential Equations, (2002), 147-154. Special Functions Approximations and Bounds via Integral Representation 35 [41] E. Mathieu, Trait´e de physique math´ematique, VI–VII: Th´eorie de l’´elasticit´e des corps solides, Gauthier-Villars, Paris, 1890. S. E. M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic Publishers, Dordrecht, 1993.

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Advances in Inequalities for Special Functions by Pietro Cerone

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