Related papers: A Note on Gamma Function and Convolution
This paper considers various integrals where the integrand includes the log gamma function (or its derivative, the digamma function) multiplied by a trigonometric or hyperbolic function. Some apparently new integrals and series are…
Fracture functions and their evolution equations are reviewed. Some phenomenological applications are briefly discussed.
In this paper, we continue studying the properties of $\gamma$-semi-continuous and $\gamma$-semi-open functions introduced in [5].
E661 in the Enestrom index. This was originally published as "Variae considerationes circa series hypergeometricas" (1776). In this paper Euler is looking at the asymptotic behavior of infinite products that are similar to the Gamma…
De Giorgi conjectured in 1979 that if a sequence of functionals converges in the sense of Gamma-convergence to a limiting functional, then the corresponding gradient flows will converge as well after changing timescale appropriately. It is…
We derive an identity for certain linear combinations of polylogarithm functions with negative exponents, which implies relations for linear combinations of Eulerian numbers. The coefficients of our linear combinations are related to…
We introduce a new factorial function which agrees with the usual Euler gamma function at both the positive integers and at all half-integers, but which is also entire. We describe the basic features of this function.
In this paper, we prove Raabe-type integral formulas for gamma function via left and right sided Riemann-Liouville fractional integrals. As corollaries, we give the left and right sided repeated integration formulas for the log-gamma and…
In this paper we introduce the concept of a convolution type operation of functionals on Wiener space. It contains several kinds of the concepts of convolution products on Wiener space, which have been studied by many authors. We then…
In this paper, we study some properties of multivariate gamma function and zonal polynomials.
Usually, convolution refers to Laplace convolution in the literature. But Mellin convolutions can yield very ueeful results. This aspect is illustrated in the coming sections. This paper deals with Mellin convolutions of products and…
De Giorgi conjectured in 1979 that if a sequence of parabolic functionals Gamma converges to a limiting functional, then the corresponding gradient flows will converge as well after changing timescale appropriately. This paper studies the…
We prove certain conjecture holds true for a finite category which has M\"obius inversion. The conjecture states a relationship between the zeta function of a finite category and the Euler characteristic of a finite category.
This paper provides a Liouville principle for integration in terms of exponential integrals and incomplete gamma functions.
We intimate deeper connections between the Riemann zeta and gamma functions than often reported and further derive a new formula for expressing the value of $\zeta(2n+1)$ in terms of zeta at other fractional points. This paper also…
A notion of evolutionary $\Gamma$-convergence of weak type is introduced for sequences of operators acting on time-dependent functions. This extends the classical definition of $\Gamma$-convergence of functionals due to De Giorgi. The…
In this paper we calculate some Generalized Selberg integrals. The answer is expressed in terms of $\Gamma$-functions. Integrals of this type serve as normalization constants or directly via undoing 2-D integrals for determination of…
We introduce Omega functions that generalize Euler Gamma functions and study the functional difference equation they satisfy. Under a natural exponential growth condition, the vector space of meromorphic solutions of the functional equation…
We prove that a certain conjecture holds true and the conjecture states a relationship between the zeta function of a finite category and the Euler characteristic of a finite category.
The present article is devoted to one example which related to the Salem function. The main attention is given to properties of one type of functions including items related to functional equations, graphs, the Lebesgue integral, etc.