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Showing posts with the label Jacobi triple product

INFINITE SERIES INVOLVING \sech^2(n \pi s)

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In this blog entry we will prove the following three results related to the Jacobi Theta function Click here for the proof. It relies on the Jacobi triple product (proved here ) And special value of Jacobi theta function (proved here )

INFINITE PRODUCTS AND JACOBI THETA FUNCTION

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This entry has some of the infinite product related to Jacobi Theta function proved. Click here to read it. The Jacobi triple product proved here , plays a central role in their proof as well some special values of the Jacobi theta function, see here

JACOBI TRIPLE PRODUCT AND PRODUCT REPRESENTATION OF JACOBI THETA FUNCTIONS

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In this entry I will prove the remarkable Jacobi triple product using one of the most elementary proofs due to great mathematician George Andrews. Additionally, it will be shown some product representations of Jacobi theta function and the beautiful Euler´s pentagonal theorem This note is an excerpt of my ongoing personal project of putting all the blog content with additional content in a book format, so if you like it or would like to leave a comment please let me know. Click here to the proof.