The general exponential integral function with
The Exponential Function
... Notice that since r < 0, the right hand side of this equation is already defined. Again, please convince yourself that the rules in (1) are valid when the exponents are any real numbers. Sketched below are the graphs ...
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ON THE EXPONENTIAL FUNCTION
... natural exponential function is one of the most important functions students should learn in calculus ...ponential function exp(x) starting from an accessible definition to the derivation of all of ...
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THE COMPLEX EXPONENTIAL FUNCTION
... Often the definition of e z is made using power series with complex numbers z but this requrires a considerable amount of preliminary work with power series... where arctan (also called [r] ...
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Univalence of a New General Integral Operator Associated with the Hypergeometric Function
... Copyright © 2013 H. Aldweby and M. Darus. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided ...
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On general Eulerian integral of certain products of A-function, and a class of polynomials
... a general Eulerian integral concerning the product of the multivariable A-functions defined by Gautam et al [1], a generalized hypergeometric function and a class of multivariable ...
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Predator Population Dynamics Involving Exponential Integral Function When Prey Follows Gompertz Model
... This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/ Abstract The current study investigates the predator-prey problem with assumptions ...
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On general Eulerian integral of certain products of A-function, the multivariable I-function and a class of polynomials
... an general Eulerian integral involving the product of the A-function defined by Gautam et al [1], the multivariable I-function defined by Nambisan et al [2], a general class of ...
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Definite Integral Relation Involving H-Function of Multivariable Function and General Class of Polynomial
... an integral relation containing to a product of Fox’s H-function [2], , general class of multivariable polynomials srivastava and Garg [11],generalized polynomials srivastava [10] and ...
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Exponential Functions: Differentiation and Integration. The Natural Exponential Function
... The familiar rules for operating with rational exponents can be extended to the natural exponential function, as shown in the following theorem. Proof To prove Property 1, you can write Because the natural ...
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EXPONENTIAL DECAY ESTIMATES FOR SINGULAR INTEGRAL OPERATORS
... the exponential decay whenever there is a superlinear rate, namely, in all the cases except for the ...a general scheme that can be applied to any pair of operators fulfilling certain general ...
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On general Eulerian integral of certain products of I-functions and multivariable A-function
... contour integral with the help of the equation ...hypergeometric function in Mellin-Barnes contour integral with the help of ...contour integral and interchange the order of integrations which ...
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On general Eulerian integral of certain products of A-functions and a multivariable Aleph-function
... Eulerian integral of most general characters associated with the products of two multivariable A-functions defined by Gautam et al [1], the Aleph-function of several variables and a generalized ...
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Majorization problems for two subclasses of analytic functions connected with the Liu–Owa integral operator and exponential function
... where r 5 := r 2 (α, β, 0) is the smallest positive root of the equation r 2 e r – | α + β – 1 | r 2 – e r – 2r + | α + β – 1 | = 0 (α ≥ 0; β > –1). (4.1) 5 Conclusions In this paper, we investigate the problems of ...
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On general Eulerian integral of certain products of multivariable A-function, the multivariable I-function and a class of polynomials
... an general Eulerian integral involving the product of the multivariable A-function, the multivariable I-function defined by Nambisan et al [3], a general class of multivariable ...
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On general Eulerian integral of certain products of multivariable A-function, the multivariable I-function and a class of polynomials
... Eulerian integral of most general characters associated with the products of two multivariable I-functions defined by Nambisan et al [3], the A-function of several variables defined by Gautam et al ...
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On general Eulerian integral of certain product multivariable A-function, the classes of polynomials and generalized hypergeometric function
... an general Eulerian integral involving the product of the multivariable A-function defined by Gautam et al [1], the general classes of multivariable polynomials and a generalized ...
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On general Eulerian integral of certain products of I-function, the multivariable Aleph-function and a class of polynomials
... an general Eulerian integral involving the product of the I-function defined by Nambisan et al [1], the multivariable Aleph-function , a general class of multivariable polynomials and a ...
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Absolute monotonicity of a function involving the exponential function
... Wang, Complete monotonicity, completely monotonic degree, integral representations, and an inequality related to the exponential, trigamma, and modified Bessel functions, Glob. Widder, T[r] ...
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ESTIMATION OF PARAMETERS AND RELIABILITY FUNCTION OF EXPONENTIATED EXPONENTIAL DISTRIBUTION: BAYESIAN APPROACH UNDER GENERAL ENTROPY LOSS FUNCTION
... Exponentiated Exponential distribution, General entropy loss function, Type II censoring, Simulated ...distribution function and survival function can not be expressed in a nice closed ...
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On general Eulerian integral of certain product of multivariable Aleph-function, the classes of polynomials and generalized hypergeometric function
... To prove (3.14), first expressing a class of multivariable polynomials defined by Srivastava [4] in serie with the help of (1.13), a class of multivariable polynomials defined by Srivastava et al [6] in serie with the ...
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