Some Laplace transforms and integral representations for parabolic cylinder functions and error functions

DOI10.15672/hujms.612642zbMath1488.33010arXiv1908.00001OpenAlexW3042956261MaRDI QIDQ5164414

Dirk Veestraeten

Publication date: 11 November 2021

Published in: Hacettepe Journal of Mathematics and Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.00001

zbMATH Keywords

Laplace transformerror functiongeneralized hypergeometric functionconfluent hypergeometric functionGaussian hypergeometric functionconvolution theoremparabolic cylinder function

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Laplace transform (44A10) Generalized hypergeometric series, ({}_pF_q) (33C20) Classical hypergeometric functions, ({}_2F_1) (33C05) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15) Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (33B20)

Cites Work

• On minimum Fisher information distributions with restricted support and fixed variance
• Some integral representations and limits for (products of) the parabolic cylinder function
• An integral representation for the product of parabolic cylinder functions
• Inequalities and monotonicity properties for zeros of Hermite functions
• Sticky reflecting Ornstein-Uhlenbeck diffusions and the Vasicek interest rate model with the sticky zero lower bound
• Torsional oscillations of longitudinally inhomogeneous coronal loops
• A table of integrals of the Error functions
• Diffusion approximation and first passage time problem for a model neuron
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