Displaying similar documents to “Operator representation of fermi-Dirac and Bose-Einstein integral functions with applications.”

On the functional properties of Bessel zeta-functions

Takumi Noda (2015)

Acta Arithmetica

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Zeta-functions associated with modified Bessel functions are introduced as ordinary Dirichlet series whose coefficients are J-Bessel and K-Bessel functions. Integral representations, transformation formulas, a power series expansion involving the Riemann zeta-function and a recurrence formula are given. The inverse Laplace transform of Weber's first exponential integral is the basic tool to derive the integral representations. As an application, we give a new proof of the Fourier series...

Integral Representations of the Logarithmic Derivative of the Selberg Zeta Function

Gušić, Dženan (2010)

Mathematica Balkanica New Series

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AMS Subj. Classification: MSC2010: 11F72, 11M36, 58J37 We point out the importance of the integral representations of the logarithmic derivative of the Selberg zeta function valid up to the critical line, i.e. in the region that includes the right half of the critical strip, where the Euler product definition of the Selberg zeta function does not hold. Most recent applications to the behavior of the Selberg zeta functions associated to a degenerating sequence of finite volume,...

A functional relation for Tornheim's double zeta functions

Kazuhiro Onodera (2014)

Acta Arithmetica

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We generalize the partial fraction decomposition which is fundamental in the theory of multiple zeta values, and prove a relation between Tornheim's double zeta functions of three complex variables. As applications, we give new integral representations of several zeta functions, an extension of the parity result to the whole domain of convergence, concrete expressions of Tornheim's double zeta function at non-positive integers and some results on the behavior of a certain Witten's zeta...