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Mock Theta Function

Ramanujan was the first to extensively study these Theta Function-like functions

$\displaystyle f(q)$ $\textstyle =$ $\displaystyle \sum_{n=0}^\infty {q^{n^2}\over (1+q)^2(1+q^2)^2\cdots(1+q^n)^2}$  
$\displaystyle \phi(q)$ $\textstyle =$ $\displaystyle \sum_{n=0}^\infty {q^{n^2}\over (1+q^2)(1+q^4)\cdots(1+q^{2n})}.$  

See also q-Series, Theta Function


References

Bellman, R. E. A Brief Introduction to Theta Functions. New York: Holt, Rinehart, and Winston, 1961.




© 1996-9 Eric W. Weisstein
1999-05-26