Formula:7541

Digital Library of Mathematical Functions ID 20.11.E5

${\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\tfrac{1}{2},\tfrac{1}{2};1;k^{2}\right)={\theta_{3}^{2}}\left(0\middle|\tau\right);}}$

Symbols List

• ${\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}$: = F ( a , b ; c ; z ) notation for Gauss’ hypergeometric function
• ${\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z}\middle|\NVar{\tau}\right)}}$:
• ${\displaystyle{\displaystyle\tau}}$: lattice parameter
• ${\displaystyle{\displaystyle k}}$: modulus (locally)
 

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