Article citationsMore>>

Hochstrasser, U.W. (1964) Chap. 22 Orthogonal Polynomials. In: Abramowitz, M. and Stegun I.A., Eds., Handbook of Mathematical Functions. Nauka, Moskva.

has been cited by the following article:

• TITLE: Duality between Bessel Functions and Chebyshev Polynomials in Expansions of Functions

  AUTHORS: Alfred Wünsche

  KEYWORDS: Spherical Bessel Functions, Chebyshev Polynomials, Legendre Polynomials, Hermite Polynomials, Derivatives of Delta Functions, Normally and Anti-Normally Ordered Operators

  JOURNAL NAME: Advances in Pure Mathematics, Vol.13 No.8, August 30, 2023

  ABSTRACT: In expansions of arbitrary functions in Bessel functions or Spherical Bessel functions, a dual partner set of polynomials play a role. For the Bessel functions, these are the Chebyshev polynomials of first kind and for the Spherical Bessel functions the Legendre polynomials. These two sets of functions appear in many formulas of the expansion and in the completeness and (bi)-orthogonality relations. The analogy to expansions of functions in Taylor series and in moment series and to expansions in Hermite functions is elaborated. Besides other special expansion, we find the expansion of Bessel functions in Spherical Bessel functions and their inversion and of Chebyshev polynomials of first kind in Legendre polynomials and their inversion. For the operators which generate the Spherical Bessel functions from a basic Spherical Bessel function, the normally ordered (or disentangled) form is found.