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Estimates for the arctangent function related to Shafer's inequality

Cristinel Mortici, H. M. Srivastava (2014)

Colloquium Mathematicae

The aim of this article is to give new refinements and sharpenings of Shafer's inequality involving the arctangent function. These are obtained by means of a change of variables, which makes the computations much easier than the classical approach.

Fractional Integration of the Product of Bessel Functions of the First Kind

Kilbas, Anatoly, Sebastian, Nicy (2010)

Fractional Calculus and Applied Analysis

Dedicated to 75th birthday of Prof. A.M. Mathai, Mathematical Subject Classification 2010:26A33, 33C10, 33C20, 33C50, 33C60, 26A09Two integral transforms involving the Gauss-hypergeometric function in the kernels are considered. They generalize the classical Riemann-Liouville and Erdélyi-Kober fractional integral operators. Formulas for compositions of such generalized fractional integrals with the product of Bessel functions of the first kind are proved. Special cases for the product of cosine...

Integration of some very elementary functions

Jan Mařík (1993)

Mathematica Bohemica

Let m be a natural number. Let f , g and Q be real polynomials such that { d e g f , d e g g } { 1 , 2 } , d e g Q < m d e g f , g is not a square and f has imaginary roots, if it is not linear. Effective methods for the integration of Q / ( f m g are exhibited.


H. Laurent (1875)

Nouvelles annales de mathématiques : journal des candidats aux écoles polytechnique et normale

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