Author | Byrd, Paul F. author |
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Title | Handbook of Elliptic Integrals for Engineers and Scientists [electronic resource] / by Paul F. Byrd, Morris D. Friedman |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1971 |
Edition | Second Edition, Revised |
Connect to | http://dx.doi.org/10.1007/978-3-642-65138-0 |
Descript | XVI, 360 p. 7 illus. online resource |
Definitions and Fundamental Relations -- 110. Elliptic Integrals -- 120. Jacobian Elliptic Functions -- 130. Jacobiโs Inverse Elliptic Functions -- 140. Jacobian Zeta Function -- 150. Heumanโs Lambda Function -- 160. Transformation Formulas for Elliptic Functions and Elliptic Integrals -- Reduction of Algebraic Integrands to Jacobian Elliptic Functions -- 200. Introduction -- 210. Integrands Involving Square Roots of Sums and Differences of Squares -- 230. Integrands Involving the Square root of a Cubic -- 250. Integrands Involving the Square root of a Quartic -- 270. Integrands Involving Miscellaneous Fractional Powers of Polynomials -- Reduction of Trigonometric Integrands to Jacobian Elliptic Functions -- Reduction of Hyperbolic Integrands to Jacobian Elliptic Functions -- Tables of Integrals of Jacobian Elliptic Functions -- 310. Recurrence Formulas for the Integrals of the Twelve Jacobian Elliptic Functions -- 330. Additional Recurrence Formulas -- 360. Integrands Involving Various Combinations of Jacobian Elliptic Functions -- 390. Integrals of Jacobian Inverse Elliptic Functions -- Elliptic Integrals of the Third Kind -- 400. Introduction -- 410. Table of Integrals -- Table of Miscellaneous Elliptic Integrals Involving Trigonometric or Hyperbolic Integrands -- 510. Single Integrals -- 530. Multiple Integrals -- Elliptic Integrals Resulting from Laplace Transformations -- Hyperelliptic Integrals -- 575. Introduction -- 576. Table of Integrals -- Integrals of the Elliptic Integrals -- 610. With Respect to the Modulus -- 630. With Respect to the Argument -- Derivatives -- 710. With Respect to the Modulus -- 730. With Respect to the Argument -- 733. With Respect to the Parameter -- Miscellaneous Integrals and Formulas -- Expansions in Series -- 900. Developments of the Elliptic Integrals -- 907. Developments of Jacobian Elliptic Functions -- 1030. Weierstrassian Elliptic Functions and Elliptic Integrals -- Definition, p. 308. โ Relation to Jacobian elliptic functions, p. 309. โ Fundamental relations, p. 309. โ Derivatives, p. 309. โ Special values, p. 310. โ Addition formulas, p. 310. โ Relation to Theta functions, p. 310. โ Weierstrassian normal elliptic integrals, p. 311. โ Other integrals, p. 312. โ Illustrative example, p. 313. -- 1050. Theta Functions -- Definitions, p. 315. โ Special values, p. 316. โ Quasi-Addition Formulas, p.317. โ Differential equation, p. 317. โ Relation to Jacobian elliptic functions, p. 318. โ Relation to elliptic integrals, p. 318. -- 1060. Pseudo-elliptic Integrals -- Definition, p. 320. โ Examples, p. 321. -- Table of Numerical Values -- Supplementary Bibliography