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Antiderivatives and Integrals Involving Incomplete Beta Functions with Applications Author(s):
R. AlAhmad^{1,2} and H. Almefleh^{1} Mathematics Department, Faculty of Engineering, Abstract:
In this paper, we prove that incomplete beta functions are antiderivatives of several products and powers of trigonometric functions, we give formulas for antiderivatives for products and powers of trigonometric functions in term of incomplete beta functions, and we evaluate integrals involving trigonometric functions using incomplete beta functions. Also, we extend some properties of the beta functions to the incomplete beta functions. As an application for the above results, we find the moments for certain probability distributions. 1: Paper Source PDF document Paper's Title:
Integrating Factors and First Integrals of a Class of Third Order Differential Equations Author(s):
Mohammadkheer AlJararha Department of Mathematics, Email: mohammad.ja@yu.edu.jo Abstract:
The principle of finding an integrating factor for a none exact differential equations is extended to a class of third order differential equations. If the third order equation is not exact, under certain conditions, an integrating factor exists which transforms it to an exact one. Hence, it can be reduced into a second order differential equation. In this paper, we give explicit forms for certain integrating factors of a class of the third order differential equations. 1: Paper Source PDF document Paper's Title:
On Finding Integrating Factors and First Integrals for a Class of Higher Order Differential Equations Author(s):
Mohammadkheer M. AlJararha Department of Mathematics, Abstract:
If the $nth$ order differential equation is not exact, under certain
conditions, an integrating factor exists which transforms the differential
equation into an exact one. Thus, the order of differential equation can be
reduced to the lower order. In this paper, we present a technique for finding
integrating factors of the following class of differential equations:
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