A radial derivative with boundary values of the spherical Poisson integral.
A recovery of Brouncker's proof for the quadrature continued fraction.
350 years ago in Spring of 1655 Sir William Brouncker on a request by John Wallis obtained a beautiful continued fraction for 4/π. Brouncker never published his proof. Many sources on the history of Mathematics claim that this proof was lost forever. In this paper we recover the original proof from Wallis' remarks presented in his Arithmetica Infinitorum. We show that Brouncker's and Wallis' formulas can be extended to MacLaurin's sinusoidal spirals via related Euler's products. We derive Ramanujan's...
A recursion formula for the moments of the gaussian orthogonal ensemble
We present an analogue of the Harer–Zagier recursion formula for the moments of the gaussian Orthogonal Ensemble in the form of a five term recurrence equation. The proof is based on simple gaussian integration by parts and differential equations on Laplace transforms. A similar recursion formula holds for the gaussian Symplectic Ensemble. As in the complex case, the result is interpreted as a recursion formula for the number of 1-vertex maps in locally orientable surfaces with a given number of...
A relation between the Laplace transform and the Mellin transform with applications
A remark on Whittaker functions on SL
We prove the recursive integral formula of class one -Whittaker functions on SL conjectured and verified in case of by Stade.
A representation of Jacobi functions.
A series transformation formula and related polynomials.
A set of orthogonal polynomials induced by a given orthogonal polynomial.
A simple method for constructing non-liouvillian first integrals of autonomous planar systems
We show that a transformation method relating planar first-order differential systems to second order equations is an effective tool for finding non-liouvillian first integrals. We obtain explicit first integrals for a subclass of Kukles systems, including fourth and fifth order systems, and for generalized Liénard-type systems.
A simple proof of Ramanujan's summation of the ... .
A simplification of the Laplace method for double integrals. Application to the second Appell function.
A solution of the boundary value problem in heat conduction
A special class of two dimensional exponential-Bessel series of Fox’s -function
A study of -Laguerre polynomials through the -operator
The present paper deals with certain generating functions and recurrence relations for -Laguerre polynomials through the use of the -operator introduced in an earlier paper [7].
A survey on D-semiclassical orthogonal polynomials.
A symbolic operator approach to power series transformation-expansion formulas.
A transplantation theorem for ultraspherical polynomials at critical index
We investigate the behaviour of Fourier coefficients with respect to the system of ultraspherical polynomials. This leads us to the study of the “boundary” Lorentz space corresponding to the left endpoint of the mean convergence interval. The ultraspherical coefficients of -functions turn out to behave like the Fourier coefficients of functions in the real Hardy space ReH¹. Namely, we prove that for any the series is the Fourier series of some function φ ∈ ReH¹ with .
A triple lacunary generating function for Hermite polynomials.
A truncated bivariate Cauchy distribution.
A Unified Group-Theoretic Method on Improper Partial Semi-Bilateral Generating Functions
2000 Mathematics Subject Classification: 33A65, 33C20.A unifed group-theoretic method of obtaining more general class of generating functions from a given class of improper partial semi-bilateral generating functions involving Laguerre and Gegenbauer polynomials are discussed.