New PDF release: Advances in Inequalities for Special Functions

By Pietro Cerone

ISBN-10: 1600219195

ISBN-13: 9781600219191

This ebook is the 1st in a set of study monographs which are dedicated to providing fresh examine, improvement and use of Mathematical Inequalities for certain capabilities. the entire papers integrated within the booklet have peen peer-reviewed and canopy various issues that come with either survey fabric of formerly released works in addition to new effects. In his presentation on precise services approximations and boundaries through quintessential illustration, Pietro Cerone utilises the classical Stevensen inequality and boundaries for the Ceby sev useful to acquire bounds for a few classical distinctive capabilities. The method will depend on selecting bounds on integrals of goods of services. The ideas are used to procure novel and worthwhile bounds for the Bessel functionality of the 1st style, the Beta functionality, the Zeta functionality and Mathieu sequence.

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Dragomir Proof. 18) (1 ≤) m m 2 j=1 zj 2 m j=1 zj provided γ ≤ zj ≤ Γ, j ∈ {1, . . , m} . 18) we have m m j=1 1 n2kj ≤ 1 nγ + n1Γ 4 n1γ · n1Γ 2  2 ≤ (Γ + γ) , 4γΓ j = 1, . 19) 1 m− 2 m 1 j=1 n2kj    m m 1 1 1  ≤ + 4 j=1 n2kj −Γ+γ j=1 n2kj −γ+Γ 1 +  2 1≤i

Dragomir, New upper and lower bounds for the Cebyˇ sev functional, J. Ineq. Pure & Appl. , 3(5) Art. 77, (2002). au/v3n5/]. 34 P. Cerone [21] P. Cerone and S. Dragomir, Generalisations of the Gr¨ uss, Chebychev and Lupa¸s inequalities for integrals over different intervals, Int. J. Appl. , 6(2) (2001), 117-128. [22] P. S. Dragomir, On some inequalities arising from Montgomery’s identity, J. Comput. Anal. , 5(4) (2003), 341-362. [23] P. S. Dragomir, On some inequalities for the expectation and variance, Korean J.

26). 43) ζ L (4k + 1) < α (2k) ζ (2k) − γ (2k) L22 (2k) , β (2k) where we have used the fact that L2 (x) < ζ (x + 1) . 44) ζ E (4k + 1) < α (2k) ζ (4k) − γ (2k) ζ 2 (2k + 2) . β (2k) 24 P. 45) β 2 (2k) + 4γ (2k) α (2k) ζ (4k) ζ Q (4k + 1) < . 00208436. 3 as demonstrated by the numerics which are presented in Table 1 of [10]. Numerical experimentation using Maple seems to indicate that the upper bounds for ζ L (4k + 1) , ζ E (4k + 1) and ζ Q (4k + 1) are in increasing order. Analytic demonstration that ζ L (4k + 1) is better remains an open problem.

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Advances in Inequalities for Special Functions by Pietro Cerone

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