Solved problems in analysis: as applied to gamma, beta, Legendre and Bessel functions
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Dover Publications
1971
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Ausgabe 1963 unter dem Titel: Solved problems: Gamma and beta functions, Legendre polynomials, Bessel functions |
| Beschreibung: | VI, 410 Seiten |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804121296638836736 |
|---|---|
| adam_text | CONTENTS
Chapter I
The Gamma Function and the Beta Function
Introduction, Table and Graph
Integral Expressions of T(x) Probs. 1 3
Properties of r(*) Probs. 4,10,12 21,31
Specific Evaluations of T(x) Probs. 5 9,11,22,23
Infinite Product Expression of r(jc) Prob. 24
T ( 1) = Negative of Euler s Constant Prob. 32
Logarithmic Derivative of T(x) for Positive Integers Prob. 33
Integral Expressions of B(jr, y) Probs. 25, 27,28
Properties of B (x, y) Probs. 26,29,30
Table of Formulas
Chapter II
Applications of the Gamma Function and the Beta Function
Introduction
Evaluation^ Integrals Probs. 1 11,14 27,33,35
r(i)=V» Probs. 12,13
Infinite Product Expression of ir/2 Probs. 28,29
Evaluation of Certain Geometrical Magnitudes Probs. 30 32,34,36 39
Evaluation of Certain Physical Quantities Probs. 36,40 42
Approximation of n for Large Integers Probs. 43 47
Two Problems in Probability Probs. 48 49
A Problem in Heat Flow in a Straight Wire Prob. 50
Chapter III
Legendre Polynomials
Introduction
Coefficients in Expansion of a Generating Function Prob. 1
Recurrence Relations Probs. 2,13 15,23,24
Laplace s Integral Expression of Pn(x) Prob. 3
Determination of Specific Legendre Polynomials Prob. 4 9
Rodrigues s Expression for Pn(x) Prob. 10
Orthogonality Property and Related Property Probs. 16,17
Expansion of a Given Function in Legendre Polynomials Probs. 11, 18, 19
P«(x) S 1 for 1 g x g 1 Prob. 12
Character and Location of Zeros of Pn(x) Prob. 21
Evaluation of Integrals Involving Legendre
Polynomials Probs. 20, 26,28 36
Evaluation of P2nW Prob. 25
vl Contents
Evaluation of Derivatives Probs. 22, 25, 27
Tables and Graph
Chapter IV
Applications of Legendre Polynomials
Introduction
Specific Series Expansions Probs. 1 8,16,17
Steady state Heat flow Temperature Distribution Probs. 9 13
Gravitational Potential of a Circular Lamina Prob. 14
Potential of an Electric Charge Distribution Prob. 15
Infinite Product Expression for ir/2 Prob. 18
Application of Gauss s Mechanical Quadrature
Formula with Pertinent Table Probs. 19 20
Chapter V
Bessel Functions
Introduction
Differentiation Formulas Probs. 1 6,8 10,12,15,19
Recursion Formulas Probs. 7,16
Specific Evaluations Probs. 13,14
Generating Functions Probs. 22,23
Orthogonality Property and Related Property Probs. 24, 25
Expansion of a Given Function in Bessel Functions Probs. 26, 27
Evaluation of Integrals Involving Bessel Functions Probs. 11, 28 33
Functions of Orders n + i Probs. 17,18,20
Alternation of Zeros Prob. 21
Approximations for Small and Large Arguments Probs. 34, 35
Integral Expression of Jp(x) and of /„(•*) Probs. 36, 37
Relations to Legendre Polynomials Probs. 38 41
Formulas and Tables
Chapter VI
Applications of Bessel Functions
Introduction
Solutions of Equations Reducible to Bessel s Equation Probs. 1 6
Specific Expansions in Bessel Functions Probs. 7 10
Problems in Dynamics Probs. 11 17,21,22
Flux Distribution in a Nuclear Reactor Prob. 18
Heat flow Temperature Distribution Probs. 19,20,24,25,30
Fluid Velocity Imparted by Radially Pulsating Cylinder Prob. 23
Displacement of Vibrating Annular Membrane Prob. 26
Alternating Current Density Prob. 27
Eddy Current Density and Power Loss Probs. 28,29
Index 406
|
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| discipline | Mathematik |
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| spelling | Farrell, Orin J. Verfasser aut Solved problems in analysis as applied to gamma, beta, Legendre and Bessel functions Orin J. Farrell, Union College, Bertram Ross, New Haven College New York, NY Dover Publications 1971 VI, 410 Seiten txt rdacontent n rdamedia nc rdacarrier Ausgabe 1963 unter dem Titel: Solved problems: Gamma and beta functions, Legendre polynomials, Bessel functions Gamma functions Problems, exercises, etc Harmonic functions Problems, exercises, etc Betafunktion (DE-588)4144960-5 gnd rswk-swf Bessel-Funktionen (DE-588)4069359-4 gnd rswk-swf Legendre-Polynome (DE-588)4333222-5 gnd rswk-swf Spezielle Funktion (DE-588)4182213-4 gnd rswk-swf Gammafunktion (DE-588)4289118-8 gnd rswk-swf 1\p (DE-588)4143389-0 Aufgabensammlung gnd-content Legendre-Polynome (DE-588)4333222-5 s DE-604 Betafunktion (DE-588)4144960-5 s Gammafunktion (DE-588)4289118-8 s Bessel-Funktionen (DE-588)4069359-4 s Spezielle Funktion (DE-588)4182213-4 s 2\p DE-604 Ross, Bertram Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004526987&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 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 | Farrell, Orin J. Ross, Bertram Solved problems in analysis as applied to gamma, beta, Legendre and Bessel functions Gamma functions Problems, exercises, etc Harmonic functions Problems, exercises, etc Betafunktion (DE-588)4144960-5 gnd Bessel-Funktionen (DE-588)4069359-4 gnd Legendre-Polynome (DE-588)4333222-5 gnd Spezielle Funktion (DE-588)4182213-4 gnd Gammafunktion (DE-588)4289118-8 gnd |
| subject_GND | (DE-588)4144960-5 (DE-588)4069359-4 (DE-588)4333222-5 (DE-588)4182213-4 (DE-588)4289118-8 (DE-588)4143389-0 |
| title | Solved problems in analysis as applied to gamma, beta, Legendre and Bessel functions |
| title_auth | Solved problems in analysis as applied to gamma, beta, Legendre and Bessel functions |
| title_exact_search | Solved problems in analysis as applied to gamma, beta, Legendre and Bessel functions |
| title_full | Solved problems in analysis as applied to gamma, beta, Legendre and Bessel functions Orin J. Farrell, Union College, Bertram Ross, New Haven College |
| title_fullStr | Solved problems in analysis as applied to gamma, beta, Legendre and Bessel functions Orin J. Farrell, Union College, Bertram Ross, New Haven College |
| title_full_unstemmed | Solved problems in analysis as applied to gamma, beta, Legendre and Bessel functions Orin J. Farrell, Union College, Bertram Ross, New Haven College |
| title_short | Solved problems in analysis |
| title_sort | solved problems in analysis as applied to gamma beta legendre and bessel functions |
| title_sub | as applied to gamma, beta, Legendre and Bessel functions |
| topic | Gamma functions Problems, exercises, etc Harmonic functions Problems, exercises, etc Betafunktion (DE-588)4144960-5 gnd Bessel-Funktionen (DE-588)4069359-4 gnd Legendre-Polynome (DE-588)4333222-5 gnd Spezielle Funktion (DE-588)4182213-4 gnd Gammafunktion (DE-588)4289118-8 gnd |
| topic_facet | Gamma functions Problems, exercises, etc Harmonic functions Problems, exercises, etc Betafunktion Bessel-Funktionen Legendre-Polynome Spezielle Funktion Gammafunktion Aufgabensammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004526987&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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