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arXiv · 1603.05512

On Certain Positive Semidefinite Matrices of Special Functions

Ruiming Zhang
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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.

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Ruiming Zhang. 2016-03-15. On Certain Positive Semidefinite Matrices of Special Functions. https://arxiv.org/abs/1603.05512

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