Tables of Mellin Transforms:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1974
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book contains tables of integrals of the Mellin transform type z-l J (a) 1> (z) q,(x)x dx o t Since the substitution x = e- transforms (a) into (b) 1> (z) the Mellin transform is sometimes referred to as the two sided Laplace transform. The use of the Mellin transform in various problems in mathematical analysis is well established. Particularly widespread and effective is its application to problems arising in analytic number theory. This is partially due to the fact that if ¢(z) corresponding to a given q,(x) by (a) is known, then ¢(z) belonging to xaq,(x) or more general to P xaq,(x ) (p real) is likewise known. (See particularly the rules in sections 1. 1 and 2. 1 of this book. ) A list of major contributions concerning Mellin transforms is added at the end of the introduction. Latin letters (unless otherwise stated) denote real positive numbers while Greek letters denote complex parameters within the given range of validity. The author is indebted to Mrs. Jolan Eross for her tireless effort and patience while typing this manuscript. Oregon State University Corvallis, Oregon May 1974 Fritz Oberhettinger Contents Part I. Mellin Transforms Introduction. . . . . . . . . . . . . . . . 1 Some Applications of the Mellin Transform Analysis. . .. . . . . . . . . . . . . . . . 6 1. 1 General Formulas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1. 2 Algebraic Functions and Powers of Arbitrary Order . . . 13 1. 3 Exponential Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
| Beschreibung: | 1 Online-Ressource (VII, 278 p) |
| ISBN: | 9783642659751 9783540069423 |
| DOI: | 10.1007/978-3-642-65975-1 |
Internformat
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| 500 | |a This book contains tables of integrals of the Mellin transform type z-l J (a) 1> (z) q,(x)x dx o t Since the substitution x = e- transforms (a) into (b) 1> (z) the Mellin transform is sometimes referred to as the two sided Laplace transform. The use of the Mellin transform in various problems in mathematical analysis is well established. Particularly widespread and effective is its application to problems arising in analytic number theory. This is partially due to the fact that if ¢(z) corresponding to a given q,(x) by (a) is known, then ¢(z) belonging to xaq,(x) or more general to P xaq,(x ) (p real) is likewise known. (See particularly the rules in sections 1. 1 and 2. 1 of this book. ) A list of major contributions concerning Mellin transforms is added at the end of the introduction. Latin letters (unless otherwise stated) denote real positive numbers while Greek letters denote complex parameters within the given range of validity. The author is indebted to Mrs. Jolan Eross for her tireless effort and patience while typing this manuscript. Oregon State University Corvallis, Oregon May 1974 Fritz Oberhettinger Contents Part I. Mellin Transforms Introduction. . . . . . . . . . . . . . . . 1 Some Applications of the Mellin Transform Analysis. . .. . . . . . . . . . . . . . . . 6 1. 1 General Formulas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1. 2 Algebraic Functions and Powers of Arbitrary Order . . . 13 1. 3 Exponential Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | ||
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Datensatz im Suchindex
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| author | Oberhettinger, Fritz |
| author_facet | Oberhettinger, Fritz |
| author_role | aut |
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| building | Verbundindex |
| bvnumber | BV042422895 |
| classification_tum | MAT 000 |
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| ctrlnum | (OCoLC)863787951 (DE-599)BVBBV042422895 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-65975-1 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642659751 9783540069423 |
| language | English |
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| spelling | Oberhettinger, Fritz Verfasser aut Tables of Mellin Transforms by Fritz Oberhettinger Berlin, Heidelberg Springer Berlin Heidelberg 1974 1 Online-Ressource (VII, 278 p) txt rdacontent c rdamedia cr rdacarrier This book contains tables of integrals of the Mellin transform type z-l J (a) 1> (z) q,(x)x dx o t Since the substitution x = e- transforms (a) into (b) 1> (z) the Mellin transform is sometimes referred to as the two sided Laplace transform. The use of the Mellin transform in various problems in mathematical analysis is well established. Particularly widespread and effective is its application to problems arising in analytic number theory. This is partially due to the fact that if ¢(z) corresponding to a given q,(x) by (a) is known, then ¢(z) belonging to xaq,(x) or more general to P xaq,(x ) (p real) is likewise known. (See particularly the rules in sections 1. 1 and 2. 1 of this book. ) A list of major contributions concerning Mellin transforms is added at the end of the introduction. Latin letters (unless otherwise stated) denote real positive numbers while Greek letters denote complex parameters within the given range of validity. The author is indebted to Mrs. Jolan Eross for her tireless effort and patience while typing this manuscript. Oregon State University Corvallis, Oregon May 1974 Fritz Oberhettinger Contents Part I. Mellin Transforms Introduction. . . . . . . . . . . . . . . . 1 Some Applications of the Mellin Transform Analysis. . .. . . . . . . . . . . . . . . . 6 1. 1 General Formulas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1. 2 Algebraic Functions and Powers of Arbitrary Order . . . 13 1. 3 Exponential Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mathematics Mathematics, general Mathematik Mellin-Transformation (DE-588)4339148-5 gnd rswk-swf 1\p (DE-588)4184303-4 Tabelle gnd-content Mellin-Transformation (DE-588)4339148-5 s 2\p DE-604 https://doi.org/10.1007/978-3-642-65975-1 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Oberhettinger, Fritz Tables of Mellin Transforms Mathematics Mathematics, general Mathematik Mellin-Transformation (DE-588)4339148-5 gnd |
| subject_GND | (DE-588)4339148-5 (DE-588)4184303-4 |
| title | Tables of Mellin Transforms |
| title_auth | Tables of Mellin Transforms |
| title_exact_search | Tables of Mellin Transforms |
| title_full | Tables of Mellin Transforms by Fritz Oberhettinger |
| title_fullStr | Tables of Mellin Transforms by Fritz Oberhettinger |
| title_full_unstemmed | Tables of Mellin Transforms by Fritz Oberhettinger |
| title_short | Tables of Mellin Transforms |
| title_sort | tables of mellin transforms |
| topic | Mathematics Mathematics, general Mathematik Mellin-Transformation (DE-588)4339148-5 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Mellin-Transformation Tabelle |
| url | https://doi.org/10.1007/978-3-642-65975-1 |
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