• Journal of the Korean Mathematical Society
• /
• v.59 no.5
• /
• pp.1015-1045
• /
• 2022

Zagier introduced the term "strange identity" to describe an asymptotic relation between a certain q-hypergeometric series and a partial theta function at roots of unity. We show that behind Zagier's strange identity lies a statement about Bailey pairs. Using the iterative machinery of Bailey pairs then leads to many families of multisum strange identities, including Hikami's generalization of Zagier's identity.

• Communications of the Korean Mathematical Society
• /
• v.37 no.2
• /
• pp.575-583
• /
• 2022

In the theory of hypergeometric and generalized hypergeometric series, the well-known and very useful identity due to Bailey (which is a generalization of the Preece's identity) plays an important role. The aim of this research paper is to provide generalizations of Bailey's identity involving products of generalized hypergeometric series in the most general form. A few known, as well as new results, have also been obtained as special cases of our main findings.

• Honam Mathematical Journal
• /
• v.38 no.1
• /
• pp.25-37
• /
• 2016

In 1972, Andrews derived the basic analogue of Gauss's second summation theorem and Bailey's theorem by implementing basic analogue of Kummer's theorem into identity due to Jackson. Recently Lavoie et.al. derived many results closely related to Kummer's theorem, Gauss's second summation theorem and Bailey's theorem and also Rakha et. al. derive the basic analogues of results closely related Kummer's theorem. The aim of this paper is to derive basic analogues of results closely related Gauss's second summation theorem and Bailey's theorem. Some applications and limiting cases are also considered.

• Kyungpook Mathematical Journal
• /
• v.59 no.2
• /
• pp.293-299
• /
• 2019

A number of identities associated with the product of generalized hypergeometric series have been investigated. In this paper, we aim to establish an identity involving the product of the generalized hypergeometric series $_2F_2$. We do this using the generalized Kummer-type II transformation due to Rathie and Pogany and another identity due to Bailey. The result presented here, being general, can be reduced to a number of relatively simple identities involving the product of generalized hypergeometric series, some of which are observed to correspond to known ones.

• Journal of Fashion Business
• /
• v.25 no.4
• /
• pp.14-35
• /
• 2021

This study compares and analyzes the designs of Burberry creative directors, Christopher Bailey and Riccardo Tisci. For this purpose, 322 photographs (176 Christopher Bailey and 146 Riccardo Tisci) were collected and the data analysis criteria were classified into color, shape, material, decoration, item, and fashion style. With respect to the data analysis method, statistical analysis and content analysis were combined. First, the design characteristics of Christopher Bailey top and bottom combined bright tone, tone-in-tone color scheme, H-line, heterogeneous material combination, and smart casual appeared very frequently. Second, the design characteristics of Riccardo Tisci top and bottom combined were monotone, tone-on-tone color scheme, H-line, heterogeneous material combinations, and street culture. Third, the design differences between creative directors were significantly different in color, tone, color arrangement, pattern, material type, material combination, detail, top and bottom items, and fashion style. Burberry men's wear maintains Burberry's traditional design identity with achromatic colors, beige-based colors, and beige checks. Christopher Bailey's design direction is characterized by modernity in a casual mood that emphasizes practicality. The design direction of Riccardo Tisci is characterized by a wide gap between images in a semi-formal style that emphasizes Burberry's tradition and a free-spirited casual style.

• Honam Mathematical Journal
• /
• v.37 no.3
• /
• pp.339-352
• /
• 2015

We aim at giving explicit expressions of $${\sum_{m,n=0}^{{\infty}}}{\frac{{\Delta}_{m+n}(-1)^nx^{m+n}}{({\rho})_m({\rho}+i)_nm!n!}$$, where i = 0, ${\pm}1$, ${\ldots}$, ${\pm}9$ and $\{{\Delta}_n\}$ is a bounded sequence of complex numbers. The main result is derived with the help of the generalized Kummer's summation theorem for the series $_2F_1$ obtained earlier by Choi. Further some special cases of the main result considered here are shown to include the results obtained earlier by Kim and Rathie and the identity due to Bailey.