Formula:7475

Digital Library of Mathematical Functions ID 20.5.E13

${\displaystyle{\displaystyle\frac{\theta_{4}'\left(z,q\right)}{\theta_{4}\left(z,q\right)}=4\sin\left(2z\right)\sum_{n=1}^{\infty}\frac{q^{2n-1}}{1-2q^{2n-1}\cos\left(2z\right)+q^{4n-2}}=4\sum_{n=1}^{\infty}\frac{q^{n}}{1-q^{2n}}\sin\left(2nz\right).}}$

Symbols List

• ${\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z},\NVar{q}\right)}}$:
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle n}}$: integer
• ${\displaystyle{\displaystyle z}}$: complex
• ${\displaystyle{\displaystyle q}}$: nome
 

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