A new identity linking coefficients of a certain class of homogeneous polynomials and Gauss hypergeometric functions
نویسندگان
چکیده
In investigating the properties of a certain class of homogeneous polynomials, we discovered an identity satisfied by their coefficients which involves simple 2F1 Gauss hypergeometric functions. This result appears to be new and we supply a direct proof. The simplicity of the identity is suggestive of a deeper result.
منابع مشابه
A Brief Determination of Certain Class of Power Semicircle Distribution
In this paper, we give a new and direct proof for the recently proved conjecture raised in Soltani and Roozegar (2012). The conjecture can be proved in a few lines via the integral representation of the Gauss-hypergeometric function unlike the long proof in Roozegar and Soltani (2013).
متن کاملA generalization of Clausen’s identity
Abstract The paper aims to generalize Clausen’s identity to the square of any Gauss hypergeometric function. Accordingly, solutions of the related 3rd order linear differential equation are found in terms of certain bivariate series that can reduce to 3F2 series similar to those in Clausen’s identity. The general contiguous variation of Clausen’s identity is found. The related Chaundy’s identit...
متن کاملIntegral Properties of Zonal Spherical Functions, Hypergeometric Functions and Invariant
Some integral properties of zonal spherical functions, hypergeometric functions and invariant polynomials are studied for real normed division algebras.
متن کاملBilinear and Bilateral Generating Functions for the Gauss’ Hypergeometric Polynomials
The object of the present paper is to investigate several general families of bilinear and bilateral generating functions with different argument for the Gauss’ hypergeometric polynomials. Mathematics Subject Classification(2010): Primary 42C05, Secondary 33C45. Keywords—Appell’s functions, Gauss hypergeometric functions, Heat polynomials, Kampe’ de Fe’riet function, Laguerre polynomials, Lauri...
متن کاملEtingof Trace, Path Hypergeometric Functions and Integrable Systems
Under a certain condition, we find the explicit formulas for the trace functions of certain intertwining operators among gl(n)-modules, introduced by Etingof in connection with the solutions of the Calogero-Sutherland model. If n = 2, the master function of the trace function is exactly the classical Gauss hypergeometric function. When n > 2, the master functions of the trace functions are a ne...
متن کامل