Handbook of Elliptic Integrals for Engineers and Scientists [Paperback]

Engineers 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.Definitions and Fundamental Relations.- 110. Elliptic Integrals.- 120. Jacobian Elliptic Functions.- 130. Jacobis Inverse Elliptic Functions.- 140. Jacobian Zeta Function.- 150. Heumans 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 Functilˆ