Formula:9401

Digital Library of Mathematical Functions ID 29.8.E5

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \LameEc{2m}{\nu}@{z_{1}}{k^{2}}\frac{w_{2}(\compellintKk@@{k})-w_{2}(-\compellintKk@@{k})}{\left.\ideriv{w_{2}(z)}{z}\right|_{z=0}}=\int_{-\compellintKk@@{k}}^{\compellintKk@@{k}}\FerrersP[]{\nu}@{y}\LameEc{2m}{\nu}@{z}{k^{2}}\diff{z},}

Symbols List

• ${\displaystyle{\displaystyle\mathit{Ec}^{\NVar{m}}_{\NVar{\nu}}\left(\NVar{z},\NVar{k^{2}}\right)}}$:
• ${\displaystyle{\displaystyle K\left(\NVar{k}\right)}}$: Legendre’s complete elliptic integral of the first kind
• ${\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}$: derivative of $$f$$ with respect to $$x$$
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\mathsf{P}_{\NVar{\nu}}\left(\NVar{x}\right)=\mathsf{P}^{0}_{\nu}\left(x\right)}}$:
• ${\displaystyle{\displaystyle m}}$: nonnegative integer
• ${\displaystyle{\displaystyle y}}$: real variable
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle k}}$: real parameter
• ${\displaystyle{\displaystyle\nu}}$: real parameter
• ${\displaystyle{\displaystyle w(z)}}$: solution
 

Resources that cite this formula

No records found.