On an expansion formula of Liu

Expansion formulas for multiple basic hypergeometric series over root systems

We extend expansion formulas of Liu given in 2013 to the context of multiple series over root systems. Liu and others have shown the usefulness of these formulas in Special Functions and number-theoretic contexts. We extend Wang and Ma's generalizations of Liu's work which they obtained using $q$-Lagrange inversion. We use the $A_n$ and $C_n$ Bailey transformation and other summation theorems due to Gustafson, Milne, Milne and Lilly, and others, from the theory of $A_n$, $C_n$ and $D_n$ basic hypergeometric series.

On the Equivalence of Fourier Expansion and Poisson Summation Formula for the Series Approximation of the Exponential Function

In this short note we show the equivalence of Fourier expansion and Poisson summation approaches for the series approximation of the exponential function $\exp ({-{t^2}/4})$. The application of the Poisson summation formula is shown to reduce to that of the Fourier expansion method.

Some Expansion Formulas for Brenke Polynomial Sets

In this paper, we derive some explicit expansion formulas associated to Brenke polynomials using operational rules based on their corresponding generating functions. The obtained coefficients are expressed either in terms of finite double sums or finite sums or sometimes in closed hypergeometric terms. The derived results are applied to Generalized Gould-Hopper polynomials and Generalized Hermite polynomials introduced by Szegö and Chihara. Some well-known duplication and convolution formulas are deduced as particular cases.

Summation, transformation, and expansion formulas for multibasic theta hypergeometric series

After reviewing some fundamental facts from the theory of theta hypergeometric series we derive, using indefinite summation, several summation, transformation, and expansion formulas for multibasic theta hypergeometric series. Some of the identities presented here generalize corresponding formulas given in Chapter 11 of the Gasper and Rahman book [Basic hypergeometric series, 2nd ed., Encyclopedia of Mathematics And Its Applications 96, Cambridge University Press, Cambridge, 2004].

倾斜Toeplitz子式的Borodin-Okounkov-Geronimo-Case恒等式

A Borodin-Okounkov-Geronimo-Case identity for tilted Toeplitz minors

本文证明了倾斜Toeplitz子式的Fredholm行列式恒等式，将BOGC恒等式推广到Hardy空间的斜分割，并应用于周期TASEP中KPZ不动点的识别。

An analogue of Gutzmer's formula for Hermite expansions

We prove an analogue of Gutzmer's formula for Hermite expansions. As a consequence we obtain a new proof of a characterisation of the image of $ L^2(\R^n) $ under the Hermite semigroup. We also obtain some new orthogonality relations for complexified Hermite functions.