On Bateman-integral functions

Chaudhuri, Jyoti

doi:10.1007/bf01195148

Cited by 2 publications

(3 citation statements)

References 3 publications

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“…. ; Res > 0 (38) where W κ,µ (z) is the Whittaker function. Formulas in (32) and (33) are accessible in a much more general forms by applying the basic properties of the Laplace transformation…”

Section: The Bateman Functions With Integer Ordersmentioning

confidence: 99%

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The Bateman Functions Revisited after 90 Years—A Survey of Old and New Results

2021

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The Bateman functions and the allied Havelock functions were introduced as solutions of some problems in hydrodynamics about ninety years ago, but after a period of one or two decades they were practically neglected. In handbooks, the Bateman function is only mentioned as a particular case of the confluent hypergeometric function. In order to revive our knowledge on these functions, their basic properties (recurrence functional and differential relations, series, integrals and the Laplace transforms) are presented. Some new results are also included. Special attention is directed to the Bateman and Havelock functions with integer orders, to generalizations of these functions and to the Bateman-integral function known in the literature.

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Section: The Bateman Functions With Integer Ordersmentioning

confidence: 99%

“…Probably, the most paying attention from generalized Bateman functions is that which was proposed by Chaudhuri [38]. In an analogy with the integral Bessel functions, he introduced the Bateman-integral function…”

Section: Introductionmentioning

confidence: 99%

The Bateman Functions Revisited after 90 Years—A Survey of Old and New Results

2021

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“…However, reviewing the papers dealing with these so-called generalized Bateman functions, Erdélyi pointed out that the integrals in (7) are particular cases of confluent hypergeometric functions and the derived mathematical expressions are not new because they follow directly from manipulations with known properties of the Kummer confluent hypergeometric functions. Probably, the most paying attention from generalized Bateman functions is that which was proposed by Chaudhuri [38]. In an analogy with the integral Bessel functions, he introduced the Bateman-integral function…”

Section: Introductionmentioning

confidence: 99%

The Bateman Functions Revisited After 90 Years -- A Survey of Old and New Results

Apelblat,

Consiglio,

Mainardi

2021

Preprint

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The Bateman functions and the allied Havelock functions were introduced as solutions of some problems in hydrodynamics about ninety years ago, but after period of one or two decades they were practically neglected. In handbooks, the Bateman function is only mentioned as a particular case of the confluent hypergeometric function. In order to revive our knowledge on these functions their basic properties (recurrence functional and differential relations, series, integrals and the Laplace transforms) are presented. Some new results are also included. Special attention is directed to the Bateman and Havelock functions with integer orders, to known in the literature generalizations of these functions and to the Bateman-integral function.

show abstract

On Bateman-integral functions

Cited by 2 publications

References 3 publications

The Bateman Functions Revisited after 90 Years—A Survey of Old and New Results

The Bateman Functions Revisited after 90 Years—A Survey of Old and New Results

The Bateman Functions Revisited After 90 Years -- A Survey of Old and New Results

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