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Tempered Relaxation Equation and Related Generalized Stable Processes
Fractional relaxation equations, as well as relaxation functions timechanged by independent stochastic processes have been widely studied (see, for...
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Non-Gaussian Measures in Infinite Dimensional Spaces: the Gamma-Grey Noise
In the context of non-Gaussian analysis, Schneider [
29 ] introduced grey noise measures, built upon Mittag-Leffler functions; analogously, grey... -
Grünbaum-Type Inequalities for Gamma and Incomplete Gamma Functions
We show that the gamma and incomplete gamma functions satisfy certain functional inequalities of Grünbaum-type. Among our results is a new...
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Some New Approximations and Proofs for Mills’ Ratio
In this paper, we present some new proofs for asymptotic series of Mills’ ratio. Given these new inequalities, the upper bound of the error of Mills’...
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Integral Representation for Bessel’s Functions of the First Kind and Neumann Series
A Fourier-type integral representation for Bessel’s functions of the first kind and complex order is obtained by using the Gegenbauer extension of...
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Extended Srivastava’s triple hypergeometric H A,p,q function and related bounding inequalities
In this paper, motivated by certain recent extensions of the Euler’s beta, Gauss’ hypergeometric and confluent hypergeometric functions (see [4]), we...
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Certain transformations for multiple hypergeometric functions
The aim of this research is to provide many new hypergeometric transformations of Kampé de Fériet’s double hypergeometric functions and Srivastava’s...
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Extension of a quadratic transformation due to Whipple with an application
The aim of this research is to provide an extension of an interesting and useful quadratic transformation due to Whipple. The result is derived with...
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Certain unified integrals associated with Bessel functions
A remarkably large number of integral formulas involving a variety of special functions have been developed by many authors. Very recently, Ali gave...
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Inequalities and Bounds for the Incomplete Gamma Function
Inequalities involving the incomplete gamma function are established. They are obtained using logarithmic convexity of some function associated with...
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Some conjectures on the zeros of approximates to the Riemann ≡-function and incomplete gamma functions
Riemann conjectured that all the zeros of the Riemann ≡-function are real, which is now known as the Riemann Hypothesis (RH). In this article we...
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Some Aspects of the Modular Relation
This paper is a companion to the forthcoming paper [19] and exhibits various manifestations of the modular relation, equivalent to the functional...
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Functional inequalities for the error function
Let erf be the error function. We determine the best possible constants $ \alpha_n $ and $ \beta_n $ such that the functional inequalities $ \alpha_n...