Cubic Analogues of the Jacobian Theta Function θ(z, q)
Cubic Analogues of the Jacobian Theta Function θ(z, q)
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DOI：
10.4153/cjm-1993-038-2
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发表时间：
1993-08
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影响因子：
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通讯作者：
M. Hirschhorn;F. Garvan;J. Borwein
中科院分区：
文献类型：
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作者：
M. Hirschhorn;F. Garvan;J. Borwein
类似于经典θ2(Q)，θ3(Q)，θ4(Q)和超几何函数的超几何函数的参数化涉及三种模形式a(Q)，b(Q)，c(Q).我们给出了类似于经典θ(z，q)的椭圆函数a(Q)，b(Q)，c(Q)的推广.证明了一些恒等式。证明是独立的，仅仅依赖于Jacobi三重乘积恒等式
Abstract There are three modular forms a(q), b(q), c(q) involved in the parametrization of the hypergeometric function analogous to the classical θ2(q), θ3(q), θ4(q) and the hypergeometric function We give elliptic function generalizations of a(q), b(q), c(q) analogous to the classical theta-function θ(z, q). A number of identities are proved. The proofs are self-contained, relying on nothing more than the Jacobi triple product identity