Summation of Some Series of Bessel Functions

Some Integrals Involving Bessel Functions Some Integrals Involving Bessel Functions

A number of new definite integrals involving Bessel functions are presented. These have been derived by finding new integral representations for the product of two Bessel functions of different order and argument in terms of the generalized hypergeometric function with subsequent reduction to special cases. Connection is made with Weber's second exponential integral and Laplace transforms of pr...

Some Distributions Involving Bessel Functions

Closed-form Summation of Some Trigonometric Series

The problem of numerical evaluation of the classical trigonometric series ^ sin(2fr+ l)a . ^ cOS(2/c + l)a ¿„(a) = > ——;-—— ana C„(a) = > —rr-,-t;—» £j (2k+1)" ÍTo Vk+XY where v > 1 in the case of Sin(a) and C2„+X(a) with n = 1, 2, 3, ... has been recently addressed by Dempsey, Liu, and Dempsey; Boersma and Dempsey; and by Gautschi. We show that, when a is equal to a rational multiple of 2k , t...

Some Inequalities for Modified Bessel Functions

We denote by Iν and Kν the Bessel functions of the first and third kind, respectively. Motivated by the relevance of the function wν t t Iν−1 t /Iν t , t > 0, in many contexts of applied mathematics and, in particular, in some elasticity problems Simpson and Spector 1984 , we establish new inequalities for Iν t /Iν−1 t . The results are based on the recurrence relations for Iν and Iν−1 and the ...

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...