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Reflection properties of zeta related functions in terms of fractional derivatives
We prove that the Weyl fractional derivative is a useful instrument to express certain properties of the zeta related functions. Specifically, we...
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On the Fractional Sums of Some Special Functions
We obtain new relations involving the Lerch transcendent and establish some closed-form expressions using special functions like the Riemann and...
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An algorithm for the evaluation of the incomplete gamma function
We introduce an algorithm for the evaluation of the Incomplete Gamma Function, P ( m , x ), for all m , x > 0. For small m , a classical recursive scheme...
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An Identity Involving Integration with Respect to Variable Order of Fractional Derivative
An identity is presented, in which an expression involving Riemann–Liouville fractional derivative is integrated with respect to the derivative’s...
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(p, q)-Extended Bessel and Modified Bessel Functions of the First Kind
Inspired by certain recent extensions of the Euler’s beta, Gauß hypergeometric and confluent hypergeometric functions (Choi et al. in Honam Math...
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Supercongruences on Truncated Hypergeometric Series
In this paper, we use p -adic Gamma function and certain formulas on hypergeometric series to establish several new supercongruences. In particular,...
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Acceleration Methods for Series: A Probabilistic Perspective
We introduce a probabilistic perspective to the problem of accelerating the convergence of a wide class of series, paying special attention to the...
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Inverses of Operator Convex Functions
The inverse of an operator convex function is shown to be operator monotone and due to the wide applications of the class of Nevanlinna’Pick...
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A Multidimensional Integral Inequality Related to Hilbert-Type Inequality
We present a multidimensional integral inequality related to the Hilbert-type inequality and the Carlson-type inequality. As an application, we...
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On Some Fractional Pearson Equations
In this paper some fractional analogues of classical Pearson differential equations are explicitly solved. Limit transitions between the solutions...
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Some applications of Retkes’ identity
We present some formulas for certain numeric sums related to the Riemann zeta function. The main tool used in our investigation is Retkes’ identity....