Abstract:Liu (Adv Math 195:1-23, 2005) derived a theta function identity. In this paper, we will give an equivalent form of Liu's identity, from which some nontrivial identities on circular summation of theta functions are deduced. Using these identities and the method of asymptotic analysis, we also derive some nontrivial finite trigonometric sum identities.
In this paper, we establish several expansion formulas for products of the Jacobi theta functions. As applications, we derive some expressions of the powers of (q;q)∞ by using these expansion formulas.
In this paper, we establish several expansion formulas for products of the Jacobi theta functions. As applications, we derive some expressions of the powers of (q;q)∞ by using these expansion formulas.
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