Multiple integrals
A Study of Multiple Integrals with Maple
... The multiple integral problem is closely related with probability theory and quantum field ...of multiple integrals by using integration term by term ...
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Studying the Problems of Multiple Integrals with Maple
... multiple integrals. The infinite series forms of the two types of multiple integrals can be obtained mainly using binomial series and integration term by term ...some multiple ...
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Representation of Multiple Integrals via the Generalized Lerch Transcendent
... of multiple integrals as linear forms in generalized polylog- ...represented multiple integrals as linear forms in 1, ζ (3), ζ(5), ...and integrals as the Euler-type multiple ...
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Multiple Integrals Transformation Involving A Generalized Multiple-Index Mittag - Leffler Function, Class of Polynomials, Multivariable Aleph-Function and Multivariable I-Function
... generalized multiple integrals transformation involving the product of a generalized multiple-index Mittag-Leffler function, multivariable Aleph-function, the multivariable I-function defined by ...
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Multiple Integrals Transformation about The Generalized Incomplete Hypergeometric Function,a General Class of Polynomials and The Multivariable Aleph-Functions
... generalized multiple integrals transformation involving the product of rhe generalized incomplete hypergeometric function, the multivariable Aleph-functions, and general class of polynomials of several ...
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Solving Multiple Integrals Using Maple
... the multiple integrals is important in probability theory and quantum field ...of multiple integrals, and we hope this method can be applied in mathematical statistics or quantum ...
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Evaluating Multiple Integrals Using Maple
... Abstract This paper uses the mathematical software Maple for the auxiliary tool to study two types of multiple integrals. We can obtain the infinite series forms of these two types of multiple ...
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A General Class of Multiple Eulerian Integrals Involving a Multivariable Gimel-Function with General Arguments
... the multiple integral formula ...Barnes multiple integrals contour representation for the multivariable Gimel-function and then interchanging the order of integrations and summations suitably, which ...
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Estimates for multiple stochastic integrals and stochastic Hamilton Jacobi equations
... for multiple integrals obtained. Multiple stochastic integrals with respect to general semimartingales or infinitely divisible pro- cesses were also considered, see ...of multiple ...
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Unification of Ramanujan Integrals with Some Infinite Integrals and Multivariable Gimel-Function
... To establish the theorem 1, expressing the multivariable Gimel-function in the Mellin-Barnes multiple integrals contour with the help of (1.1) and interchanging the order of integrations which is justified ...
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Some Expansions for a Multivariable Gimel-Function
... To establish the theorem 1, expressing the multivariable Gimel-function in the Mellin-Barnes multiple integrals contour with the help of (1.1) and interchanging the order of integrations[r] ...
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Some Results Involving Generalized Multivariable Gimel-Function and Gegenbauer Polynomials
... Expressing the generalized multivariable Gimel-function on the left sand side of (3.1) as Mellin-Barnes multiple integrals contour with the the help of (1.1), inter[r] ...
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On a Fractional Differential Operator Involving Multivariable Gimel-Function and Product of General Class of Polynomials
... We first express the multivariable gimel-function by this multiple integrals contour with the help of (1.1), express the general class of mutivariable polynomials occurring on the left-hand side of (3.1) in ...
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A Double Expansion Formula for Generalized Multivariable Gimel-Function Involving Jacobi Polynomials and Bessel Functions
... Evaluate the inner integral with the help of lemma 2 and interpreting the Mellin-Barnes multiple integrals contour in terms of the multivariable Gimel-function, we get the desired res[r] ...
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Double Fourier Cosine-Jacobi Series for Generalized Multivariable Gimel-Function
... Evaluate the inner integral with the help of lemma 1 and interpreting the Mellin-Barnes multiple integrals contour in terms of the generalized multivariable Gimel-function, we get the[r] ...
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Integral Representations and Algebraic Decompositions of the Fox-Wright Type of Special Functions
... These multiple integrals can be denoted as generalized fractional differeitegrals [6], however this line of representation is superfluous to the necessities of the numerical (i.e. Euler [r] ...
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Introduction to Real Analysis
... tiple integrals are defined in Section ...the multiple integral of a function whose discontinuities form a set of Jordan content ...in multiple integrals, and finally a careful statement and ...
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Analytical solutions of incomplete elliptic integrals motivated by the work of Ramanujan
... in theorems (3.1) to (3.12), using some algebraic properties of Pochhammer symbol and interpreting the mul- tiple power series in hypergeometric forms of Gauss [34, p. 42(1)], Kamp´e de F´eriet [34, p.63(16); see also ...
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Behavior of a Scale Factor for Wiener Integrals and a Fourier Stieltjes Transform on the Wiener Space
... [11] Kim, Y.S. (1998) A Change of Scale Formula for Wiener Integrals of Cylinder Func- tions on the Abstract Wiener Space. International Journal of Mathematics and Ma- thematical Sciences , 21, 73-78. ...
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The Multiple Gamma Functions and the Log Gamma Integrals
... In this paper, motivated by the above, we proceed in another direction to developing some generalizations of the above integrals considered by Srivastava and Choi 7. For q- analogues of the results, compare the ...
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