2016/03/15 by Ruiming Zhang, Zhang, Ruiming
Mathematics · #Mathematical Inequalities and Applications #Mathematical functions and polynomials #Advanced Mathematical Identities
paper · pdf · doi:10.48550/arxiv.1603.05512
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.