Handbook of Elliptic Integrals for Engineers and Scientists

Definitions and Fundamental Relations.- 110. Elliptic Integrals.- 120. Jacobian Elliptic Functions.- 130. Jacobi's Inverse Elliptic Functions.- 140. Jacobian Zeta Function.- 150. Heuman's 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. - Relation to Jacobian elliptic functions, p. 309. - Fundamental relations, p. 309. - Derivatives, p. 309. - Special values, p. 310. - Addition formulas, p. 310. - Relation to Theta functions, p. 310. - Weierstrassian normal elliptic integrals, p. 311. - Other integrals, p. 312. - Illustrative example, p. 313..- 1050. Theta Functions.- Definitions, p. 315. - Special values, p. 316. - Quasi-Addition Formulas, p.317. - Differential equation, p. 317. - Relation to Jacobian elliptic functions, p. 318. - Relation to elliptic integrals, p. 318..- 1060. Pseudo-elliptic Integrals.- Definition, p. 320. - Examples, p. 321..- Table of Numerical Values.- Supplementary Bibliography.