Sharp Becker-Stark-type inequalities for Bessel functions.
Sidon sets and Riesz sets for some measure algebras on the disk
Sidon sets for the disk polynomial measure algebra (the continuous disk polynomial hypergroup) are described completely in terms of classical Sidon sets for the circle; an analogue of the F. and M. Riesz theorem is also proved.
Siebzehntheilung des Lemniscatenumfangs durch alleinige Anwendung von Lineal und Cirkel.
Signed words and permutations. III: The MacMahon Verfahren.
Singular eigenfunctions of Calogero-Sutherland type systems and how to transform them into regular ones.
Singular values, Ramanujan modular equations, and Landen transformations
A new connection between geometric function theory and number theory is derived from Ramanujan’s work on modular equations. This connection involves the function recurrent in the theory of plane quasiconformal maps. Ramanujan’s modular identities yield numerous new functional identities for for various primes p.
SO(2,1)-Invariant Double Integral Transforms and Formulas for the Whittaker Functions
MSC 2010: 33C15, 33C05, 33C45, 65R10, 20C40The paper contains some new formulas involving the Whittaker functions and arising as the values of some double integrals, which are invariant with respect to the representation of the group SO(2; 1).
Sobolev orthogonal polynomials: Interpolation and approximation.
Software for the algorithmic work with orthogonal polynomials and special functions.
Solution of option pricing equations using orthogonal polynomial expansion
We study both analytic and numerical solutions of option pricing equations using systems of orthogonal polynomials. Using a Galerkin-based method, we solve the parabolic partial differential equation for the Black-Scholes model using Hermite polynomials and for the Heston model using Hermite and Laguerre polynomials. We compare the obtained solutions to existing semi-closed pricing formulas. Special attention is paid to the solution of the Heston model at the boundary with vanishing volatility.
Solution of Space-Time Fractional Schrödinger Equation Occurring in Quantum Mechanics
Dedicated to Professor A.M. Mathai on the occasion of his 75-th birthday. Mathematics Subject Classi¯cation 2010: 26A33, 44A10, 33C60, 35J10.The object of this article is to present the computational solution of one-dimensional space-time fractional Schrödinger equation occurring in quantum mechanics. The method followed in deriving the solution is that of joint Laplace and Fourier transforms. The solution is derived in a closed and computational form in terms of the H-function. It provides an elegant...
Solution of Volterra-type integro-differential equations with a generalized Lauricella confluent hypergeometric function in the kernels.
Solutions of an ordinary differential equation as a class of Fourier kernels.
Solutions of Fractional Diffusion-Wave Equations in Terms of H-functions
MSC 2010: 35R11, 42A38, 26A33, 33E12The method of integral transforms based on joint application of a fractional generalization of the Fourier transform and the classical Laplace transform is utilized for solving Cauchy-type problems for the time-space fractional diffusion-wave equations expressed in terms of the Caputo time-fractional derivative and the Weyl space-fractional operator. The solutions obtained are in integral form whose kernels are Green functions expressed in terms of the Fox H-functions....
Solvable optimal control of Brownian motion in symmetric spaces and spherical polynomials
Solvable rational potentials and exceptional orthogonal polynomials in supersymmetric quantum mechanics.
Solving Ramanujan's differential equations for Eisenstein series via a first order Riccati equation
Some applications and numerical methods for orthogonal polynomials
Some applications of a differential subordination.
Some applications of differential subordination to a general class of multivalently analytic functions involving a convolution structure.