On Certain Positive Semidefinite Matrices of Special Functions

Abstract

Special functions are often defined as a Fourier or Laplace transform of a positive measure, and the positivity of the measure manifests as positive definiteness of certain matrices. The purpose of this expository note is to give a sample of such positive definite matrices to demonstrate this connection for some well-known special functions such as Gamma, Beta, hypergeometric, theta, elliptic, zeta and basic hypergeometric functions.