Digital Library of Mathematical Functions
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20 Theta FunctionsProperties

§20.8 Watson’s Expansions

20.8.1 θ2(0,q)θ3(z,q)θ4(z,q)θ2(z,q)=2n=-(-1)nqn22nzq-n-z+qnz.

See Watson (1935a). This reference and Bellman (1961, pp. 46–47) include other expansions of this type.