Date of Award
Master of Science (MS)
Mohamed El Bachraoui
Ho Hon Leung
The object of this report is q-series and their relationship with certain special functions. Firstly, Jackson’s q-analogue of the Euler gamma function is introduced and a q-analogue for a famous formula of Gauss on products of the gamma function will be presented. Secondly, Jacobi’s theta functions will be discussed in details and new Landenlike half argument formulas will be established. As an application, q-trigonometric formulas shall be derived and a new proof for a well-known q-series relation of Jacobi will be given. Thirdly, an extended Bailey transform will be presented and a variety of new q-series will be deduced as a consequence. Some of these new formulas lead to the positivity of alternating sums of q-series.
Abo Touk, Sarah, "THE Q-GAUSS PRODUCT, Q-TRIGONOMETRY VIA LANDEN-LIKE IDENTITIES, AND POSITIVE ALTERNATING Q-SERIES" (2021). Theses. 803.