Related papers: A short table of generating functions and related …
The following material was created with the idea of being used for an introductory fractional calculus course. A recapitulation of the history of fractional calculus is presented, as well as the different attempts at fractional derivatives…
We introduce the concept of Type-I/II generating functionals defined on the space of boundary data of a Lagrangian field theory. On the Lagrangian side, we define an analogue of Jacobi's solution to the Hamilton-Jacobi equation for field…
The structure functions of the Lagrangian gauge algebra are given explicitly in terms of the hamiltonian constraints and the first order Hamiltonian structure functions and their derivatives.
The functional relation of the Hurwitz zeta function is proved by using the connection problem of the confluent hypergeometric equation.
In the present work we explore relationships between multiplicative functions defined in \cite{Garonzi_2018}, \cite{Lazorec}. To do so, we use other important quotients defined and studied in \cite{ndeg}, \cite{Marius}, thus establishing…
New proofs of the duplication formulae for the gamma and the Barnes double gamma functions are derived using the Hurwitz zeta function. Concise derivations of Gauss's multiplication theorem for the gamma function and a corresponding one for…
We first summarize joint work on several preliminary canonical Lambert series factorization theorems. Within this article we establish new analogs to these original factorization theorems which characterize two specific primary cases of the…
Aggregation functions are generally defined and used to combine several numerical values into a single one, so that the final result of the aggregation takes into account all the individual values in a given manner. Such functions are…
The first aim of this paper is to construct new generating functions for the generalized {\lambda}-Stirling type numbers of the second kind, generalized array type polynomials and generalized Eulerian type polynomials and numbers, attached…
In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones
The functional relation coming from the $x-y$ symplectic transformation of Topological Recursion has a lot of applications, for instance it is the higher order moment-cumulant relation in free probability or can be used to compute…
An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic…
We introduce a systematic approach to express generating functions for the enumeration of maps on surfaces of high genus in terms of a single generating function relevant to planar surfaces. Central to this work is the comparison of two…
An integral formula is developed which applies to an essentially arbitrary function. An application is made to the Riemann zeta function.
The concept of permutograph is introduced and properties of integral functions on permutographs are established. The central result characterizes the class of integral functions that are representable as lattice polynomials. This result is…
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…
This paper proposes a single form for statistical models that accommodates a broad range of models, from ordinary least squares to agent-based microsimulations. The definition makes it almost trivial to define morphisms to transform and…
On the one hand the Fermi-Dirac and Bose-Einstein functions have been extended in such a way that they are closely related to the Riemann and other zeta functions. On the other hand the Fourier transform representation of the gamma and…
This paper is an enhanced version of a more than decade-older paper with a similar title. Many formulae involving both finite and infinite sums of digamma and polygamma functions up to quadratic order, few of which appear in standard…
The graph of a real symplectic linear transformation is an R-Lagrangian subspace of a complex symplectic vector space. The restriction of the complex symplectic form is thus purely imaginary and may be expressed in terms of the generating…