Handbook of Elliptic Integrals for Engineers and ScientistsEngineers and physicists are more and more encountering integrations involving nonelementary integrals and higher transcendental functions. Such integrations frequently involve (not always in immediately re cognizable form) elliptic functions and elliptic integrals. The numerous books written on elliptic integrals, while of great value to the student or mathematician, are not especially suitable for the scientist whose primary objective is the ready evaluation of the integrals that occur in his practical problems. As a result, he may entirely avoid problems which lead to elliptic integrals, or is likely to resort to graphical methods or other means of approximation in dealing with all but the simplest of these integrals. It became apparent in the course of my work in theoretical aero dynamics that there was a need for a handbook embodying in convenient form a comprehensive table of elliptic integrals together with auxiliary formulas and numerical tables of values. Feeling that such a book would save the engineer and physicist much valuable time, I prepared the present volume. |
Contents
Definitions and Fundamental Relations | 8 |
P | 20 |
Conformal Mappings p 28 Applications p | 28 |
Addition | 34 |
Other transformations p | 40 |
Reduction of Trigonometric Integrands to Jacobian Elliptic Functions | 162 |
Reduction of Hyperbolic Integrands to Jacobian Elliptic Functions | 182 |
Tables of Integrals of Jacobian Elliptic Functions | 191 |
Elliptic Integrals Resulting from Laplace Transformations | 249 |
Integrals of the Elliptic Integrals | 272 |
Derivatives | 282 |
Miscellaneous Integrals and Formulas | 288 |
Expansions in Series | 298 |
Appendix | 308 |
Theta Functions | 315 |
Table of Numerical Values | 322 |
Elliptic Integrals of the Third Kind | 223 |
Table of Miscellaneous Elliptic Integrals Involving Trigonometric or Hyperbolic | 240 |
Bibliography | 351 |
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Handbook of Elliptic Integrals for Engineers and Physicists Paul F. Byrd,Morris D. Friedman Limited preview - 2013 |
Common terms and phrases
a₁ a₂ a² g a² sn² u)m b₁ b₁)² Byrd and Friedman cn u dn cn² cn2 u dn² cn2 u du cn2m cos² cosh dc² dn² u du dn² udu dn2m dt a² dt g dt t² elliptic integrals Formulas g sn² g U1 gu₁ hyperelliptic integral Integrands involving Jacobian elliptic functions k₁ k² sin² k² sin² q k² sn k² t² m₁ nc² nd² P₁ R₁ R₂ rational function sd² sin2 sin² 9 sinh sn u cn sn u₁ sn² u cn2 sn² u dn² sn2m t₁ ť² t2 dt table of integrals tm dt tn² u₁ U1 dt U1 g U1 sn² u₂ V₁ V₂ Va+b Va² Y₁ α² ατ นา