Chebyshev polynomials of the first kind and the univariate Lommel function: Integral representations

Abstract

This study investigates a number of integrals possessing products of different indices of the univariate Lommel function, sμ,ν(a){s}_{\mu ,\nu }\left(a), with various elementary and special functions. As a consequence, connections between the function and Chebyshev polynomials of the first kind are established.

Keywords

• bessel function
• chebyshev polynomial of the first kind
• fourier transform
• generalized hypergeometric function
• index/order integral
• lommel function
• parameter
• special functions
• 33c47
• 44a15
• 44a20