Jacobi's derivative formula with modular forms of level five

Kazuhide Matsuda

Published 2016-10-17Version 1

In this paper, we derive another expressions of Jacobi's derivative formula in terms of modular forms of level five. For this purpose, we use the residue theorem and the Fourier series expansions of $\eta^5(\tau)/\eta(5\tau)$ and $\eta^5(5\tau)/\eta(\tau),$ where $\eta(\tau)$ is the Dedekind eta function.