Asymptotics and Mellin-Barnes integrals:
Asymptotics and Mellin-Barnes Integrals, first published in 2001, provides an account of the use and properties of a type of complex integral representation that arises frequently in the study of special functions typically of interest in classical analysis and mathematical physics. After developing...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2001
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications
volume 85 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | Asymptotics and Mellin-Barnes Integrals, first published in 2001, provides an account of the use and properties of a type of complex integral representation that arises frequently in the study of special functions typically of interest in classical analysis and mathematical physics. After developing the properties of these integrals, their use in determining the asymptotic behaviour of special functions is detailed. Although such integrals have a long history, the book's account includes recent research results in analytic number theory and hyperasymptotics. The book also fills a gap in the literature on asymptotic analysis and special functions by providing a thorough account of the use of Mellin-Barnes integrals that is otherwise not available in other standard references on asymptotics |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xvi, 422 pages) |
| ISBN: | 9780511546662 |
| DOI: | 10.1017/CBO9780511546662 |
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| 100 | 1 | |a Paris, R. B. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Asymptotics and Mellin-Barnes integrals |c R.B. Paris, D. Kaminski |
| 246 | 1 | 3 | |a Asymptotics & Mellin-Barnes Integrals |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2001 | |
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| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 505 | 8 | 0 | |t Order Relations |t Asymptotic Expansions |t Other Expansions |t Biographies of Mellin and Barnes |t Fundamental Results |t The Gamma Function [Gamma] (z) |t The Asymptotic Expansion of [Gamma] (z) |t The Stirling Coefficients |t Bounds for [Gamma] (z) |t Expansion of Quotients of Gamma Functions |t Inverse Factorial Expansions |t A Recursion Formula when [alpha subscript r] = [beta subscript r] |t An Algebraic Method for the Determination of the A[subscript j] |t Special Cases |t The Asymptotic Expansion of Integral Functions |t Convergence of Mellin-Barnes Integrals |t Order Estimates for Remainder Integrals |t Lemmas |t Properties of Mellin Transforms |t Basic Properties |t Translational and Differential Properties |t The Parseval Formula |t Analytic Properties |t Inverse Mellin Transforms |t Integrals Connected with e[superscript -z] |t Some Standard Integrals |t Discontinuous Integrals |t Gamma-Function Integrals |t Ramanujan-Type Integrals |t Barnes' Lemmas |t Mellin-Barnes Integral Representations |t The Confluent Hypergeometric Functions |t The Gauss Hypergeometric Function |t Some Special Functions |t Applications of Mellin Transforms |t Transformation of Series |t The Mellin Transform Method |t The Poisson-Jacobi Formula |t An Infinite Series |t A Smoothed Dirichlet Series |t A Finite Sum |t Number-Theoretic Examples |t A Harmonic Sum |t Euler's Product |t Ramanujan's Function |t Some Other Number-Theoretic Sums |t Solution of Differential Equations |t Potential Problems in Wedge-Shaped Regions |
| 520 | |a Asymptotics and Mellin-Barnes Integrals, first published in 2001, provides an account of the use and properties of a type of complex integral representation that arises frequently in the study of special functions typically of interest in classical analysis and mathematical physics. After developing the properties of these integrals, their use in determining the asymptotic behaviour of special functions is detailed. Although such integrals have a long history, the book's account includes recent research results in analytic number theory and hyperasymptotics. The book also fills a gap in the literature on asymptotic analysis and special functions by providing a thorough account of the use of Mellin-Barnes integrals that is otherwise not available in other standard references on asymptotics | ||
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Datensatz im Suchindex
| _version_ | 1804176883681591296 |
|---|---|
| any_adam_object | |
| author | Paris, R. B. |
| author_facet | Paris, R. B. |
| author_role | aut |
| author_sort | Paris, R. B. |
| author_variant | r b p rb rbp |
| building | Verbundindex |
| bvnumber | BV043941655 |
| classification_rvk | SK 450 SK 470 |
| collection | ZDB-20-CBO |
| contents | Order Relations Asymptotic Expansions Other Expansions Biographies of Mellin and Barnes Fundamental Results The Gamma Function [Gamma] (z) The Asymptotic Expansion of [Gamma] (z) The Stirling Coefficients Bounds for [Gamma] (z) Expansion of Quotients of Gamma Functions Inverse Factorial Expansions A Recursion Formula when [alpha subscript r] = [beta subscript r] An Algebraic Method for the Determination of the A[subscript j] Special Cases The Asymptotic Expansion of Integral Functions Convergence of Mellin-Barnes Integrals Order Estimates for Remainder Integrals Lemmas Properties of Mellin Transforms Basic Properties Translational and Differential Properties The Parseval Formula Analytic Properties Inverse Mellin Transforms Integrals Connected with e[superscript -z] Some Standard Integrals Discontinuous Integrals Gamma-Function Integrals Ramanujan-Type Integrals Barnes' Lemmas Mellin-Barnes Integral Representations The Confluent Hypergeometric Functions The Gauss Hypergeometric Function Some Special Functions Applications of Mellin Transforms Transformation of Series The Mellin Transform Method The Poisson-Jacobi Formula An Infinite Series A Smoothed Dirichlet Series A Finite Sum Number-Theoretic Examples A Harmonic Sum Euler's Product Ramanujan's Function Some Other Number-Theoretic Sums Solution of Differential Equations Potential Problems in Wedge-Shaped Regions |
| ctrlnum | (ZDB-20-CBO)CR9780511546662 (OCoLC)849885005 (DE-599)BVBBV043941655 |
| dewey-full | 515/.723 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.723 |
| dewey-search | 515/.723 |
| dewey-sort | 3515 3723 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511546662 |
| format | Electronic eBook |
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| id | DE-604.BV043941655 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511546662 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350625 |
| oclc_num | 849885005 |
| open_access_boolean | |
| owner | DE-12 DE-92 |
| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (xvi, 422 pages) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Paris, R. B. Verfasser aut Asymptotics and Mellin-Barnes integrals R.B. Paris, D. Kaminski Asymptotics & Mellin-Barnes Integrals Cambridge Cambridge University Press 2001 1 online resource (xvi, 422 pages) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications volume 85 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Order Relations Asymptotic Expansions Other Expansions Biographies of Mellin and Barnes Fundamental Results The Gamma Function [Gamma] (z) The Asymptotic Expansion of [Gamma] (z) The Stirling Coefficients Bounds for [Gamma] (z) Expansion of Quotients of Gamma Functions Inverse Factorial Expansions A Recursion Formula when [alpha subscript r] = [beta subscript r] An Algebraic Method for the Determination of the A[subscript j] Special Cases The Asymptotic Expansion of Integral Functions Convergence of Mellin-Barnes Integrals Order Estimates for Remainder Integrals Lemmas Properties of Mellin Transforms Basic Properties Translational and Differential Properties The Parseval Formula Analytic Properties Inverse Mellin Transforms Integrals Connected with e[superscript -z] Some Standard Integrals Discontinuous Integrals Gamma-Function Integrals Ramanujan-Type Integrals Barnes' Lemmas Mellin-Barnes Integral Representations The Confluent Hypergeometric Functions The Gauss Hypergeometric Function Some Special Functions Applications of Mellin Transforms Transformation of Series The Mellin Transform Method The Poisson-Jacobi Formula An Infinite Series A Smoothed Dirichlet Series A Finite Sum Number-Theoretic Examples A Harmonic Sum Euler's Product Ramanujan's Function Some Other Number-Theoretic Sums Solution of Differential Equations Potential Problems in Wedge-Shaped Regions Asymptotics and Mellin-Barnes Integrals, first published in 2001, provides an account of the use and properties of a type of complex integral representation that arises frequently in the study of special functions typically of interest in classical analysis and mathematical physics. After developing the properties of these integrals, their use in determining the asymptotic behaviour of special functions is detailed. Although such integrals have a long history, the book's account includes recent research results in analytic number theory and hyperasymptotics. The book also fills a gap in the literature on asymptotic analysis and special functions by providing a thorough account of the use of Mellin-Barnes integrals that is otherwise not available in other standard references on asymptotics Mellin transform Asymptotic expansions Mellin-Transformation (DE-588)4339148-5 gnd rswk-swf Asymptotik (DE-588)4126634-1 gnd rswk-swf Asymptotik (DE-588)4126634-1 s Mellin-Transformation (DE-588)4339148-5 s 1\p DE-604 Kaminski, D. 1960- Sonstige oth Erscheint auch als Druckausgabe 978-0-521-79001-7 https://doi.org/10.1017/CBO9780511546662 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Paris, R. B. Asymptotics and Mellin-Barnes integrals Order Relations Asymptotic Expansions Other Expansions Biographies of Mellin and Barnes Fundamental Results The Gamma Function [Gamma] (z) The Asymptotic Expansion of [Gamma] (z) The Stirling Coefficients Bounds for [Gamma] (z) Expansion of Quotients of Gamma Functions Inverse Factorial Expansions A Recursion Formula when [alpha subscript r] = [beta subscript r] An Algebraic Method for the Determination of the A[subscript j] Special Cases The Asymptotic Expansion of Integral Functions Convergence of Mellin-Barnes Integrals Order Estimates for Remainder Integrals Lemmas Properties of Mellin Transforms Basic Properties Translational and Differential Properties The Parseval Formula Analytic Properties Inverse Mellin Transforms Integrals Connected with e[superscript -z] Some Standard Integrals Discontinuous Integrals Gamma-Function Integrals Ramanujan-Type Integrals Barnes' Lemmas Mellin-Barnes Integral Representations The Confluent Hypergeometric Functions The Gauss Hypergeometric Function Some Special Functions Applications of Mellin Transforms Transformation of Series The Mellin Transform Method The Poisson-Jacobi Formula An Infinite Series A Smoothed Dirichlet Series A Finite Sum Number-Theoretic Examples A Harmonic Sum Euler's Product Ramanujan's Function Some Other Number-Theoretic Sums Solution of Differential Equations Potential Problems in Wedge-Shaped Regions Mellin transform Asymptotic expansions Mellin-Transformation (DE-588)4339148-5 gnd Asymptotik (DE-588)4126634-1 gnd |
| subject_GND | (DE-588)4339148-5 (DE-588)4126634-1 |
| title | Asymptotics and Mellin-Barnes integrals |
| title_alt | Asymptotics & Mellin-Barnes Integrals Order Relations Asymptotic Expansions Other Expansions Biographies of Mellin and Barnes Fundamental Results The Gamma Function [Gamma] (z) The Asymptotic Expansion of [Gamma] (z) The Stirling Coefficients Bounds for [Gamma] (z) Expansion of Quotients of Gamma Functions Inverse Factorial Expansions A Recursion Formula when [alpha subscript r] = [beta subscript r] An Algebraic Method for the Determination of the A[subscript j] Special Cases The Asymptotic Expansion of Integral Functions Convergence of Mellin-Barnes Integrals Order Estimates for Remainder Integrals Lemmas Properties of Mellin Transforms Basic Properties Translational and Differential Properties The Parseval Formula Analytic Properties Inverse Mellin Transforms Integrals Connected with e[superscript -z] Some Standard Integrals Discontinuous Integrals Gamma-Function Integrals Ramanujan-Type Integrals Barnes' Lemmas Mellin-Barnes Integral Representations The Confluent Hypergeometric Functions The Gauss Hypergeometric Function Some Special Functions Applications of Mellin Transforms Transformation of Series The Mellin Transform Method The Poisson-Jacobi Formula An Infinite Series A Smoothed Dirichlet Series A Finite Sum Number-Theoretic Examples A Harmonic Sum Euler's Product Ramanujan's Function Some Other Number-Theoretic Sums Solution of Differential Equations Potential Problems in Wedge-Shaped Regions |
| title_auth | Asymptotics and Mellin-Barnes integrals |
| title_exact_search | Asymptotics and Mellin-Barnes integrals |
| title_full | Asymptotics and Mellin-Barnes integrals R.B. Paris, D. Kaminski |
| title_fullStr | Asymptotics and Mellin-Barnes integrals R.B. Paris, D. Kaminski |
| title_full_unstemmed | Asymptotics and Mellin-Barnes integrals R.B. Paris, D. Kaminski |
| title_short | Asymptotics and Mellin-Barnes integrals |
| title_sort | asymptotics and mellin barnes integrals |
| topic | Mellin transform Asymptotic expansions Mellin-Transformation (DE-588)4339148-5 gnd Asymptotik (DE-588)4126634-1 gnd |
| topic_facet | Mellin transform Asymptotic expansions Mellin-Transformation Asymptotik |
| url | https://doi.org/10.1017/CBO9780511546662 |
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