Unification of the Quintuple and Septuple Product Identities
نویسندگان
چکیده
By combining the functional equation method with Jacobi’s triple product identity, we establish a general equation with five free parameters on the modified Jacobi theta function, which can be considered as the common generalization of the quintuple, sextuple and septuple product identities. Several known theta function formulae and new identities are proved consequently.
منابع مشابه
Two Finite Forms of Watson's Quintuple Product Identity and Matrix Inversion
Recently, Chen-Chu-Gu [4] and Guo-Zeng [6] found independently that Watson’s quintuple product identity follows surprisingly from two basic algebraic identities, called finite forms of Watson’s quintuple product identity. The present paper shows that both identities are equivalent to two special cases of the q-Chu-Vandermonde formula by using the (f, g)-inversion.
متن کاملA constructive theory of triple and quintuple product identities of the second degree
The groundwork for a theory of quadratic identities involving the classical triple and quintuple products is layed. The approach is through the study and use of affine maps that act on indexing lattices associated with the terms (double sums) in the given identity. The terms of the identity are found to be connected by the invariant of a ternary quadratic form.
متن کاملLinear quintuple-product identities
In the first part of this paper, series and product representations of four single-variable triple products T0, T1, T2, T3 and four single-variable quintuple products Q0, Q1, Q2, Q3 are defined. Reduced forms and reduction formulas for these eight functions are given, along with formulas which connect them. The second part of the paper contains a systematic computer search for linear trinomial ...
متن کاملهویت و تأثیر آن بر سیاست خارجیِ یمن در دوران پسا اتحاد 1990
After the 1990 unification in Yemen, the country’s officials made efforts to adopt a new turn of behaviors in various areas, especially their foreign policy, in accordance to the created changes to prove themselves to their peripheral and international environments. Based thereupon, they did their best to define a new identity for the unified Yemen and identify their foreign policy and behavior...
متن کاملEasy Computer Proofs of the Rogers - RamanujanIdentities and of Identities of Similar
New short and easy computer proofs of nite versions of the Rogers-Ramanujan identities and of similar type are given. These include a very short proof of the rst Rogers-Ramanujan identity that was missed by computers, and a new proof of the well-known quintuple product identity by creative telescoping.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Electr. J. Comb.
دوره 14 شماره
صفحات -
تاریخ انتشار 2007