Some identities of Lah–Bell polynomials

Some Identities for Chandrasekhar Polynomials

Basic techniques of linear algebra are used to derive some identities involving the Chandrasekhar polynomials that play a vital role in the spherical-harmonics (A) solution to basic radiative-transfer problems. @ 1997 Elsevier Science Ltd. All rights reserved

Some Identities of the Frobenius-Euler Polynomials

and Applied Analysis 3 If n ∈ Nwith n ≡ 0 mod 2 , then we have I−1 fn − I−1 f 2 n−1 ∑ l 0 −1 l−1f l . 2.6 From 1.4 and 2.3 , we derive ∫ Zp eqdμ−1 x 2 2 q 1 − −q −1 et − −q −1 2 2 q ∞ ∑ n 0 Hn −q−1 t n n! . 2.7 Thus, we note that ∫ Zp xqdμ−1 x 2 2 q Hn −q−1 , ∫ Zp y x qdμ−1 x 2 2 q Hn −q−1, x . 2.8 Let n ∈ N with n ≡ 1 mod 2 . Then we obtain 2 q n−1 ∑ l 0 −1 ql qHm −q−1, n Hm −q−1 . 2.9 For n ∈...

Some Plethystic Identities And Kostka-Foulkes Polynomials

plays an important role in the Garsia-Haglund proof of the q, t-Catalan conjecture, [2]. Let ΛQ(q,t) be the space of symmetric functions of degree n, over the field of rational functions Q(q, t), and let ∇ : ΛQ(q,t) → Λ n Q(q,t) be the Garsia-Bergeron operator. By studying recursions, Garsia and Haglund show that the coefficient of the elementary symmetric function en(X) in the image ∇(En,k(X))...

Jack Polynomials and Some Identities for Partitions

We prove an identity about partitions involving new combinatorial coefficients. The proof given is using a generating function. As an application we obtain the explicit expression of two shifted symmetric functions, related with Jack polynomials. These quantities are the moments of the “α-content” random variable with respect to some transition probability distributions.

Some identities involving generalized Gegenbauer polynomials