Evaluation of some non-elementary integrals involving the generalized hypergeometric function with some applications

26 May 2020 Nijimbere Victor

The indefinite integral $$ \int x^\alpha e^{\eta x^\beta}\,_pF_q (a_1, a_2, \cdot\cdot\cdot a_p; b_1, b_2, \cdot\cdot\cdot, b_q; \lambda x^{\gamma})dx, $$ where $\alpha, \eta, \beta, \lambda, \gamma\ne0$ are real or complex constants and $_pF_q$ is the generalized hypergeometric function, is evaluated in terms of an infinite series involving the generalized hypergeometric function. Related integrals in which the exponential function $e^{\eta x^\beta}$ is either replaced by the hyperbolic function $\cosh\left(\eta x^\beta\right)$ or $\sinh\left(\eta x^\beta\right)$, or the sinusoidal function $\cos\left(\eta x^\beta\right)$ or $\sin\left(\eta x^\beta\right)$, are also evaluated in terms of infinite series involving the generalized hypergeometric function $_pF_q$... (read more)

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