Infinite integrals involving products of Legendre functions
نویسندگان
چکیده
منابع مشابه
An Automatic Integration of Infinite Range Integrals Involving Bessel Functions
An efficient automatic quadrature procedure is developed for numerically computing the integrals 0 , where the function is smooth and nonoscillatory at infinity and is the Bessel functions of order ν =1,0 and 1/4. The procedure involves the use of an automatic integration scheme of modified FFT used for evaluating Fourier integrals and product type integration, and the modified W-transformation...
متن کاملSome 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...
متن کاملClosed Analytical Expressions for Some Useful Sums and Integrals Involving Legendre Functions
In Ref. [ 1 ] we have obtained in three different ways the components of the vector magnetic potential (VMP) for the toroidal solenoid. As they satisfy the same equations and the same boundary conditions, they should coincide everywhere (see, e.g., [2]). By comparing these components one can derive simple closed analytical expressions for some integrals and sums involving Legendre functions. Th...
متن کاملComputation of infinite integrals involving Bessel functions of arbitrary order by the/)-Transformation
The /9-transformation due to the author is an effective extrapolation method for computing infinite oscillatory integrals of various kinds. In this work two new variants of this transformation are designed for computing integrals of the form f,,~ ,q(t)cC(t)dt, where g(x) is a nonoscillatory function and %(x) may be an arbitrary linear combination of the Bessel functions of the first and second ...
متن کاملThe plane wave expansion, infinite integrals and identities involving spherical Bessel functions
This paper shows that the plane wave expansion can be a useful tool in obtaining analytical solutions to infinite integrals over spherical Bessel functions and the derivation of identites for these functions. The integrals are often used in nuclear scattering calculations, where an analytical result can provide an insight into the reaction mechanism. A technique is developed whereby an integral...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the Glasgow Mathematical Association
سال: 1957
ISSN: 2040-6185,2051-2104
DOI: 10.1017/s2040618500033554