A Lagrangian method for indefinite q-integrals
Abstract
A Lagrangian method is introduced recently for deriving indefinite integrals of special functions that satisfy homogeneous (nonhomogeneous) second-order linear differential equations. This paper extends this method to include indefinite Jackson q-integrals of special functions satisfying homogeneous (nonhomogeneous) second-order linear q-difference equations. Many q-integrals, both previously known and completely new, are derived using the method. We introduce samples of indefinite and definite q-integrals for Jackson's q-Bessel functions, q-hypergeometric functions, and some orthogonal polynomials.
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