Kummer transformations
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11—20 of 24 matching pages
11: Bibliography M
12: Bibliography C
13: 18.17 Integrals
§18.17(v) Fourier Transforms
… ►Jacobi
… ►Ultraspherical
… ►§18.17(vi) Laplace Transforms
… ►§18.17(vii) Mellin Transforms
…14: 13.4 Integral Representations
15: Bibliography T
16: 9.10 Integrals
17: 15.10 Hypergeometric Differential Equation
18: Bibliography D
19: Bibliography Z
20: Errata
A note about the multivalued nature of the Kummer confluent hypergeometric function of the second kind on the right-hand side of (7.18.10) was inserted.
There have been extensive changes in the notation used for the integral transforms defined in §1.14. These changes are applied throughout the DLMF. The following table summarizes the changes.
Transform | New | Abbreviated | Old |
---|---|---|---|
Notation | Notation | Notation | |
Fourier | |||
Fourier Cosine | |||
Fourier Sine | |||
Laplace | |||
Mellin | |||
Hilbert | |||
Stieltjes |
Previously, for the Fourier, Fourier cosine and Fourier sine transforms, either temporary local notations were used or the Fourier integrals were written out explicitly.
There were clarifications made in the conditions on the parameter in of those equations.
The equality has been added to the original equation to express an explicit connection between the two standard solutions of Kummer’s equation. Note also that the notation has been changed to .
Reported 2015-02-10 by Adri Olde Daalhuis.
The equality has been added to the original equation to express an explicit connection between the two standard solutions of Kummer’s equation.
Reported 2015-02-10 by Adri Olde Daalhuis.