Related papers: A note on a generalized circular summation formula…
Transmutation is a technique for extending classical probability distributions in order to give them more flexibility. In this paper, we are interested in cubic transmutations of the Pareto distribution. We establish a general formula that…
A method for describing the quantum kink states in the semi-classical limit of several (1+1)-dimensional field theoretical models is developed. We use the generalized zeta function regularization method to compute the one-loop quantum…
We prove a general form of Green Formula and Cauchy Integral Theorem for arbitrary closed rectifiable curves in the plane.
The axiomatic formulation of quantum field theory (QFT) of the 1950's in terms of fields defined as operator valued Schwartz distributions is re-examined in the light of subsequent developments. These include, on the physical side, the…
In the present paper authors introduce the L_n-integral transform and the inverse integral transform for n = 2^k, k=0,1,2,..., as a generalization of the classical Laplace transform and the inverse Laplace transform, respectively.…
The aim of this research is to provide thirty-two interesting summation formulas for the Kamp\'e de F\'eriet function in general forms, which are given in sixteen theorems. The results are established with the help of the identities in Liu…
The present article is devoted to the generalized Salem functions, the generailed shift operator, and certain related problems. A description of further investigations of the author of this article is given.These investigations (in terms of…
Combining the derivative operator with a binomial sum from the telescoping method, we establish a family of summation formulas involving generalized harmonic numbers.
In this comment it is pointed out that the perturbative dynamics of general massive field theories can be mapped to delimited sums of determined integral functions. The limits on the sums are the remaining obstacle to finding the general…
We write down the functional equation of the zeta function of a global field. This equation is implicit in Weil's ``Basic Number Theory''.
A formula for the Hurwitz zeta function at the positive integers $k$, $\zeta(k,b)$, is created by solving the real and the imaginary parts separately and then combining them. A few different formulae for the Hurwitz zeta function are known…
In the explicit formula for the signed mock theta functions $\Phi^{(-)[m,s]}$ obtained from the coroot lattice of $D(2,1;a)$, functions with indefinite quadratic forms naturally take place. We compute their modular transformation properties…
In this paper, we find a new recurrence formula fo the Euler zeta functions.
This paper uses the convolution theorem of the Laplace transform to derive new inverse Laplace transforms for the product of two parabolic cylinder functions in which the arguments may have opposite sign. These transforms are subsequently…
We propose generalized Fermat's conjecture in the framework of arithmetic dynamics, and give evidences. The multi-indexed version is added.
It is noted that the Legendre transformations in the standard formulation of quantum field theory have the form of functional Clairaut-type equations. It is shown that in presence of composite fields the Clairaut-type form holds after loop…
It is known that not all summation methods are linear and stable. Zeta function regularization is in general non-linear. However, in some cases formal manipulations with "zeta function" regularization (assuming linearity of sums) lead to…
We define a new class of generating function transformations related to polylogarithm functions, Dirichlet series, and Euler sums. These transformations are given by an infinite sum over the $j^{th}$ derivatives of a sequence generating…
In terms of the derivative operator, integral operator and Saalsch\"{u}tz's theorem, two families of summation formulae involving generalized harmonic numbers are established.
We generalize the standard combinatorial techniques of toric geometry to the study of log Calabi-Yau surfaces. The character and cocharacter lattices are replaced by certain integral linear manifolds described by Gross, Hacking, and Keel,…