Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

Transformation of Products of υ-Functions


Affiliations
1 Madras Christian College, India
     

   Subscribe/Renew Journal


We shall adopt the following well-known notations for υ-functions:

q = eπiτ, Imτ > o ;

υ2 (x|τ) = Σ q(n+1/2)2(2n+2)xπi,

υ (x|τ) = Σ qn2 e2nxπi,

υ (x|τ) = Σ (-I)nqn2 e2nπi.

Here, as well as in the sequel, Σ denotes summation over all integers from -∞ to +∞.


Subscription Login to verify subscription
User
Notifications
Font Size


Abstract Views: 216

PDF Views: 0




  • Transformation of Products of υ-Functions

Abstract Views: 216  |  PDF Views: 0

Authors

P. Kesava Menon
Madras Christian College, India

Abstract


We shall adopt the following well-known notations for υ-functions:

q = eπiτ, Imτ > o ;

υ2 (x|τ) = Σ q(n+1/2)2(2n+2)xπi,

υ (x|τ) = Σ qn2 e2nxπi,

υ (x|τ) = Σ (-I)nqn2 e2nπi.

Here, as well as in the sequel, Σ denotes summation over all integers from -∞ to +∞.