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Springer Tracts in Natural Philosophy

The Confluent Hypergeometric Function

with Special Emphasis on its Applications

Authors: Buchholz, Herbert

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About this book

The subject of this book is the higher transcendental function known as the confluent hypergeometric function. In the last two decades this function has taken on an ever increasing significance because of its use in the application of mathematics to physical and technical problems. There is no doubt that this trend will continue until the general theory of confluent hypergeometric functions becomes familiar to the majority of physicists in much the same way as the cylinder functions, which were previously less well known, are now used in many engineering and physical problems. This book is intended to further this development. The important practical significance of the functions which are treated hardly demands an involved discussion since they include, as special cases, a number of simpler special functions which have long been the everyday tool of the physicist. It is sufficient to mention that these include, among others, the logarithmic integral, the integral sine and cosine, the error integral, the Fresnel integral, the cylinder functions and the cylinder function in parabolic cylindrical coordinates. For anyone who puts forth the effort to study the confluent hypergeometric function in more detail there is the inestimable advantage of being able to understand the properties of other functions derivable from it. This gen­ eral point of view is particularly useful in connection with series ex­ pansions valid for values of the argument near zero or infinity and in connection with the various integral representations.

Table of contents (7 chapters)

Table of contents (7 chapters)
  • The Various Forms of the Differential Equation for the Confluent Hypergeometric Function and the Definitions of their Solutions

    Pages 1-58

    Buchholz, Professor Dr.-Ing. Herbert

  • General Integral Representations of Parabolic Functions and of their Products

    Pages 59-89

    Buchholz, Professor Dr.-Ing. Herbert

  • The Asymptotic, Behaviour of the Parabolic Functions

    Pages 90-111

    Buchholz, Professor Dr.-Ing. Herbert

  • Indefinite and Definite Integrals Involving Parabolic Functions and Some Infinite Series

    Pages 112-134

    Buchholz, Professor Dr.-Ing. Herbert

  • Polynomials Related to the Parabolic Functions and Infinite Series Based on these Polynomials

    Pages 135-155

    Buchholz, Professor Dr.-Ing. Herbert

Buy this book

eBook 64,19 €
price for Spain (gross)
  • ISBN 978-3-642-88396-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 77,99 €
price for Spain (gross)
  • ISBN 978-3-642-88398-9
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
The Confluent Hypergeometric Function
Book Subtitle
with Special Emphasis on its Applications
Authors
Translated by
Wetzel, K., Lichtblau, H.
Series Title
Springer Tracts in Natural Philosophy
Series Volume
15
Copyright
1969
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-88396-5
DOI
10.1007/978-3-642-88396-5
Softcover ISBN
978-3-642-88398-9
Series ISSN
0081-3877
Edition Number
1
Number of Pages
XVIII, 239
Topics

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