-
Chapter
Elliptic Integrals Resulting from Laplace Transformations
Finding the Laplace transform1 of products of Bessel functions2 often leads to the evaluation of elliptic integrals. We shall give here, however, only a short table of such integrals.
-
Book
-
Chapter
Miscellaneous Integrals and Formulas
While most of the integrals in the previous sections have at least one variable upper limit, both of the limits of integration of the integrals given here are fixed.
-
Chapter
Miscellaneous Elliptic Integrals Involving Trigonometric and Hyperbolic Integrands
-
Chapter
Introduction
Integrals of the form \( \int {R\left[ {t,\sqrt {{P\left( t \right)}} } \right]} dt \) , where P(t) is a polynomial of the thir...
-
Chapter
Hyperelliptic Integrals
-
Chapter
Reduction of Hyperbolic Integrands to Jacobian Elliptic Functions
-
Chapter
Derivatives
-
Chapter
Elliptic Integrals of the Third Kind
-
Chapter
Expansions in Series
-
Chapter
Definitions and Fundamental Relations
-
Chapter
Reduction of Trigonometric Integrands to Jacobian Elliptic Functions
Various elliptic integrals involving trigonometric integrands occur in many geometrical and physical problems. In order to evaluate a variety of these we again find it convenient to express them in terms of in...
-
Chapter
Integrals of the Elliptic Integrals
-
Chapter
Table of Integrals of Jacobian Elliptic Functions
In the foregoing sections, where elliptic integrals having diverse algebraic, trigonometric, and hyperbolic integrands were reduced to those involving elliptic functions, it is seen that certain standard integ...
-
Chapter
Reduction of Algebraic Integrands to Jacobian Elliptic Functions
-
Book
-
Chapter
Elliptic Integrals Resulting from Laplace Transformations
Finding the Laplace transform1 of products of Bessel functions2 often leads to the evaluation of elliptic integrals. We shall give here, however, only a short table of such integrals.
-
Chapter
Introduction
Integrals of the form <m:math display='block'> <m:mrow> <m:mstyle displaystyle='true'> <m:mrow><m:mo>∫</m:mo> <m:mrow> <m:mi>R</m:mi><m:mrow><m:mo>[</m:mo> <m:mrow> <m:mi>t</m:mi><m:mo>,</m...
-
Chapter
Integrals of the Elliptic Integrals
-
Chapter
Miscellaneous Integrals and Formulas
While most of the integrals in the previous sections have at least one variable upper limit, both of the limits of integration of the integrals given here are fixed.