منابع مشابه
Definite Integrals using Orthogonality and Integral Transforms
We obtain definite integrals for products of associated Legendre functions with Bessel functions, associated Legendre functions, and Chebyshev polynomials of the first kind using orthogonality and integral transforms.
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We adopt the following rules: r, x, y are real numbers, i, j are natural numbers, and p is a finite sequence of elements of R. The following proposition is true (1) For every closed-interval subset A of R and for every x holds x ∈ A iff inf A ¬ x and x ¬ supA. Let I1 be a finite sequence of elements of R. We say that I1 is non-decreasing if and only if the condition (Def. 1) is satisfied. (Def....
متن کاملSome new results using Hadamard fractional integral
Fractional calculus is the field of mathematical analysis which deals with the investigation and applications of integrals and derivatives of arbitrary order. The purpose of this work is to use Hadamard fractional integral to establish some new integral inequalities of Gruss type by using one or two parameters which ensues four main results . Furthermore, other integral inequalities of reverse ...
متن کاملFractional Generalization of Kac Integral
Kac integral [1, 2, 3] appears as a path-wise presentation of Brownian motion and shortly becomes, with Feynman approach [4], a powerful tool to study different processes described by the wave-type or diffusion-type equations. In the basic papers [1, 4], the paths distribution was based on averaging over the Wiener measure. It is worthwhile to mention the Kac comment that the Wiener measure can...
متن کاملFRACTIONAL CALCULUS : Integral and Differential Equations of Fractional Order
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ژورنال
عنوان ژورنال: Fractal and Fractional
سال: 2017
ISSN: 2504-3110
DOI: 10.3390/fractalfract1010002