Related papers: A generalization of Clausen's identity
We find an integral representation for the generalized hypergeometric function unifying known representations via generalized Stieltjes, Laplace and cosine Fourier transforms. Using positivity conditions for the weight in this…
The paper is devoted to a comprehensive second-order study of a remarkable class of convex extended-real-valued functions that is highly important in many aspects of nonlinear and variational analysis, specifically those related to…
We give examples of infinite order rational transformations that leave linear differential equations covariant. These examples are non-trivial yet simple enough illustrations of exact representations of the renormalization group. We first…
An implicit solution to the vanishing of the so-called Universal Field Equation, or Bordered Hessian, which dates at least as far back as 1935 \cite{chaundy} is revived, and derived from a much later form of the solution. A linear ansatz…
The Capelli identities claim $det(A)det(B) = det(AB+correction)$ for certain matrices with noncommutative entries. They have applications in representation theory and integrable systems. We propose new examples of these identities,…
The Gauss-Bonnet curvature of order $2k$ is a generalization to higher dimensions of the Gauss-Bonnet integrand in dimension $2k$, as the usual scalar curvature generalizes the two dimensional Gauss-Bonnet integrand. In this paper, we…
We give a local parametric description of all holomorphic hypersurfaces in complex Euclidean and projective spaces with constant index of relative nullity, together with applications. This is a complex analogue to the parametrization for…
We give the general solution of the Ward identity for the linear vector supersymmetry which characterizes all topological models. Such solution, whose expression is quite compact and simple, greatly simplifies the study of theories…
We relate certain universal curvature identities for Kaehler manifolds to the Euler-Lagrange equations of the scalar invariants which are defined by pairing characteristic forms with powers of the Kaehler form.
In the last decades, the theory of digamma function has been developed with a high impact of interest by many authors. Here, we established some interesting results for digamma function, and also we have computed the values of digamma…
In this paper, we give the generic classification of the singularities of 3-parameter line congruences in $\mathbb{R}^4$. We also classify the generic singularities of Blaschke (affine) normal congruences.
A generalization of Newton's identity on symmetric functions is given. Using the generalized Newton identity we give a unified method to show the existence of Hall-Littlewood, Jack and Macdonald polynomials. We also give a simple proof of…
We consider a new identity involving integrals and sums of Bessel functions. The identity provides new ways to evaluate integrals of products of two Bessel functions. The identity is remarkably simple and powerful since the summand and…
The theoretical computing of special values assumed by the hypergeometric functions has a high interest not only on its own, but also in sight of the remarkable implications to both pure Mathematics and Mathematical Physics. Accordingly, in…
It is proved that the Laurent expansion of the following Gauss hypergeometric functions, 2F1(I1+a*epsilon, I2+b*ep; I3+c*epsilon;z), 2F1(I1+a*epsilon, I2+b*epsilon;I3+1/2+c*epsilon;z), 2F1(I1+1/2+a*epsilon, I2+b*epsilon; I3+c*epsilon;z),…
In this article we provide with combinatorial proofs of some recent identities due to Sury and McLaughlin. We show that, the solution of a general linear recurrence with constant coefficients can be interpreted as a determinant of a matrix.…
In this paper, we define new generalized k-Mersenne numbers and give a formula of generalized Mersenne polynomials and further we study their properties. Moreover, we define Gaussian Mersenne numbers and obtain some identities like Binet…
There is a one-to-one correspondence between associated families of generic conformally flat (local-)hypersurfaces in 4-dimensional space forms and conformally flat 3-metrics with the Guichard condition. In this paper, we study the space of…
In this note, we aim to provide generalizations of (i) Knuth's old sum (or Reed Dawson identity) and (ii) Riordan's identity using a hypergeometric series approach.
Reduction formulas for sums of products of hypergeometric functions can be traced back to Euler. This topic has an intimate connection to summation and transformation formulas, contiguous relations and algebraic properties of the…