Indefinite integrals of incomplete elliptic integrals from Jacobi elliptic functions
Sign Up to like & getrecommendations! Published in 2017 at "Integral Transforms and Special Functions"
DOI: 10.1080/10652469.2017.1304938
Abstract: ABSTRACT Integration formulas are derived for the three canonical Legendre elliptic integrals. These formulas are obtained from the differential equations satified by these elliptic integrals when the independent variable u is the argument of Jacobian… read more here.
Keywords: integrals incomplete; elliptic integrals; indefinite integrals; incomplete elliptic ... See more keywords
More indefinite integrals from Riccati equations
Sign Up to like & getrecommendations! Published in 2019 at "Integral Transforms and Special Functions"
DOI: 10.1080/10652469.2019.1647538
Abstract: ABSTRACT Two new methods for obtaining indefinite integrals of a special function using Riccati equations are presented. One method uses quadratic fragments of the Riccati equation, the solutions of which are given by simple quadratic… read more here.
Keywords: cylinder functions; riccati equations; indefinite integrals; integrals riccati ... See more keywords
Indefinite integrals of special functions from integrating factors
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DOI: 10.1080/10652469.2019.1689567
Abstract: ABSTRACT Some general integrals are presented which were obtained from two integrating factors and for the first two and last two terms, respectively, of the second-order linear ordinary differential equation obeyed by many special functions.… read more here.
Keywords: integrating factors; functions integrating; indefinite integrals; integral transforms ... See more keywords
Indefinite integrals from Wronskians and related linear second-order differential equations
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DOI: 10.1080/10652469.2021.1938025
Abstract: Many indefinite integrals are derived for Bessel functions and associated Legendre functions from particular transformations of their differential equations which are closely linked to Wronskians. A large portion of the results for Bessel functions is… read more here.
Keywords: indefinite integrals; differential equations; wronskians related; integrals wronskians ... See more keywords