Sum of fourth powers of Jacobi theta 2 and Jacobi theta 4 equals fourth power of Jacobi theta 3

Theorem

The following formula holds: $$\vartheta_2^4(0,q)+\vartheta_4^4(0,q)=\vartheta_3^4(0,q),$$ where $\vartheta_2$ denotes the Jacobi theta 2, $\vartheta_4$ denotes the Jacobi theta 4, and $\vartheta_3$ denotes the Jacobi theta 3.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $16.28.5$