I would like to find a formula for
$$f(x) = \prod_{n=0}^{\infty} (1 + x^n)$$
$$g(x) = \prod_{n=0}^{\infty} (1 - x^n)$$
In particular, $f(1/4)$ appears as the normalization factor for the CORDIC, the coefficients of $f(x)$ gives, coefficient gives the number of partitions of n into distinct parts; number of partitions of n into odd parts.1.
I only know that that these functions can be expressed in terms of q-Pochhammer symbol.
Are there closed forms for $f(x)$ and $g(x)$ in terms of common functions. In particular, can $f(1/4)$ be expressed in a closed form?
Are there general any solutions for the finite products that could have some advantage compared to this definition?