Ramanujan theta function

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The Ramanujan theta function, $f$, is defined for $|ab|<1$ by $$f(a,b)=\displaystyle\sum_{k=-\infty}^{\infty} a^{\frac{k(k+1)}{2}} b^{\frac{k(k-1)}{2}}.$$

Properties

RamanujanTheta(a,b)=(-a;ab)_inf (-b;ab)_inf (ab;ab)_inf
RamanujanTheta(q,q)=sum q^(k^2)
RamanujanTheta(q,q)=(-q;q^2)_inf^2 (q^2;q^2)_inf

References