Formula:942

Digital Library of Mathematical Functions ID 2.8.E35

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle W_{n,3}(u,\xi)=|\xi|^{1/2}\BesselJ{\nu}@{u|\xi|^{1/2}}\sum_{s=0}^{n-1}\frac{A_{s}(\xi)}{u^{2s}}-|\xi|\BesselJ{\nu+1}@{u|\xi|^{1/2}}\sum_{s=0}^{n-2}\frac{B_{s}(\xi)}{u^{2s+1}}+|\xi|^{1/2}\envBesselJ{\nu}@{u|\xi|^{1/2}}\bigO@{\frac{1}{u^{2n-1}}},}

Symbols List

• ${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Bessel function of the first kind
• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle\mathrm{env}\mskip-2.0mu J_{\NVar{\nu}}\left(\NVar{x}\right)}}$:
• ${\displaystyle{\displaystyle W_{n,j}(u,\xi)}}$: 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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