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Showing 1 to 6 of 6 for “"Hurwitz zeta function"”.
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Higher Derivatives of the Hurwitz Zeta Function
<p>The Riemann zeta function ζ(s) is one of the most fundamental functions in number theory. Euler demonstrated that ζ(s) is closely connected to the prime numbers and Riemann gave proofs of the basic analytic properties of the zeta function. Values of the zeta function and its derivatives have …
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Transformation formulas associated with integrals involving the Riemann Ξ-function and rank-crank type PDEs in partition theory
… formulas involving various special functions such as the digamma function, Hurwitz zeta function and modified Bessel functions, through integrals involving the Riemann $\Xi$-function. Our motivation is a beautiful formula involving the digamma and the Riemann $\Xi$-functions found on …
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Discrete universality theorems for the Riemann and Hurwitz zeta-functions /
… to the discrete universality of the Riemann and Hurwitz zeta-functions and , , , which are defined, for , by the series and and by analytic continuation elsewhere, are considered. Let be the space of analytic functions on equipped with the topology of uniform convergence on compacta, be the class …
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Diskrečiosios universalumo teoremos Rymano ir Hurvico dzeta funkcijoms /
… to the discrete universality of the Riemann and Hurwitz zeta-functions and , , , which are defined, for , by the series and and by analytic continuation elsewhere, are considered. Let be the space of analytic functions on equipped with the topology of uniform convergence on compacta, be the class …
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Analysis in Fractional Calculus and Asymptotics Related to Zeta Functions
… properties of their own. Fractional calculus and zeta functions have rarely been united in research, but one chapter below covers a new formula expressing the Lerch zeta function as a fractional derivative of an elementary function. This result could have many ramifications in both fields, which …
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Weighted Universality Theorems for the Riemann and Hurwitz Zeta-Functions /
… are often investigated. Weighted universality of zeta-functions is comparatively a new branch of universality, there exist only few papers in that direction. Therefore, it was important to continue investigation of weighted universality of the classical Riemann and Hurwitz zeta-functions. Also, …