An integral formula for generalized Gegenbauer polynomials and Jacobi polynomials

An Integral Formula for Generalized Gegenbauer Polynomials and Jacobi Polynomials

Jacobi–trudy Formula for Generalised Schur Polynomials

X iv :0 90 5. 25 57 v2 [ m at h. R T ] 1 0 Ju n 20 09 JACOBI–TRUDY FORMULA FOR GENERALISED SCHUR POLYNOMIALS A.N. SERGEEV AND A.P. VESELOV Abstract. Jacobi–Trudy formula for a generalisation of Schur polynomials related to any sequence of orthogonal polynomials in one variable is given. As a corollary we have Giambelli formula for generalised Schur polynomials.

The Addition Formula for Jacobi Polynomials

Recently the author derived a Laplace integral representation, a product formula and an addition formula for Jacobi polynomials Ppfi). The results are (1) (2) and (3) * j, ,I " (~0~2 0-f-2 sin2 0 + ir cos #I sin 28)n * ' P$ycos 281) PFycos 282) 2&x + 1) Pgq 1) Pfq 1)-= l/22 qa-p)r(/l+#. . .

Some identities involving generalized Gegenbauer polynomials

A Product Formula for Jacobi Polynomials