Ramanujan theta function

From specialfunctionswiki
Jump to: navigation, search

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[edit]

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[edit]