Formula:932

Digital Library of Mathematical Functions ID 2.8.E26

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle W_{n,2}(u,\xi)=\xi^{1/2}\modBesselK{\nu}@{u\xi^{1/2}}\sum_{s=0}^{n-1}\frac{A_{s}(\xi)}{u^{2s}}-\xi\modBesselK{\nu+1}@{u\xi^{1/2}}\sum_{s=0}^{n-2}\frac{B_{s}(\xi)}{u^{2s+1}}+\xi^{1/2}\modBesselK{\nu}@{u\xi^{1/2}}\bigO@{\frac{1}{u^{2n-1}}}.}

Symbols List

• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}$: modified Bessel function of the second kind
• ${\displaystyle{\displaystyle W_{n,j}(u,\xi)}}$: solution
• ${\displaystyle{\displaystyle\nu}}$: real nonnegative constant
• ${\displaystyle{\displaystyle n}}$: positive integer
• ${\displaystyle{\displaystyle A_{s}(\xi)}}$: coefficients
• ${\displaystyle{\displaystyle B_{s}(\xi)}}$: coefficients
• ${\displaystyle{\displaystyle u}}$: large real or complex parameter
 

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