DLMF:14.5.E22

MaRDI QIDQ5431

• Label: DLMF:14.5.E22

Digital Library of Mathematical Functions ID 14.5.E22

${\displaystyle{\displaystyle\mathsf{Q}_{\frac{1}{2}}\left(\cos\theta\right)=K\left(\cos\left(\tfrac{1}{2}\theta\right)\right)-2E\left(\cos\left(\tfrac{1}{2}\theta\right)\right),}}$

Symbols List

• ${\displaystyle{\displaystyle K\left(\NVar{k}\right)}}$: Legendre’s complete elliptic integral of the first kind
• ${\displaystyle{\displaystyle E\left(\NVar{k}\right)}}$: Legendre’s complete elliptic integral of the second kind
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle\mathsf{Q}_{\NVar{\nu}}\left(\NVar{x}\right)=\mathsf{Q}^{0}_{\nu}\left(x\right)}}$:
• ${\displaystyle{\displaystyle 0<\theta<\pi}}$: variable
 

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