q-Sumudu Transforms ofq-Analogues of Bessel Functions

q-Sumudu Transforms of q-Analogues of Bessel Functions

The main purpose of this paper is to evaluate q-Sumudu transforms of a product of q-Bessel functions. Interesting special cases of theorems are also discussed. Further, the results proved in this paper may find certain applications of q-Sumudu transforms to the solutions of the q-integrodifferential equations involving q-Bessel functions. The results may help to extend the q-theory of orthogona...

Steep polyominoes, q-Motzkin numbers and q-Bessel functions

We introduce three deenitions of the q-analogs of Motzkin numbers and illustrate some combinatorial interpretations of these q-numbers. We relate the rst class of q-numbers to the steep parallelogram polyominoes' generating function according to their width, perimeter and area. We show that this generating function is the quotient of two q-Bessel functions. The second class of q-Motzkin numbers...

Analogues for Bessel Functions of the Christoffel-Darboux Identity

We derive analogues for Bessel functions of what is known as the Christoffel-Darboux identity for orthonormal polynomials: ∞ ∑ k=1 2 (ν + k) Jν+k(w) Jν+k(z) = wz w − z ( Jν+1(w) Jν(z)− Jν(w) Jν+1(z) )

Interpolation Analogues of Schur Q-functions

We introduce interpolation analogues of Schur Q-functions — the multiparameter Schur Q-functions. We obtain for them several results: a combinatorial formula, generating functions for one-row and two-rows functions, vanishing and characterization properties, a Pieri-type formula, a Nimmo-type formula (a relation of two Pfaffians), a Giambelli-Schur-type Pfaffian formula, a determinantal formula...

A note on the comparison between Laplace and Sumudu transforms