Formula:6414

Digital Library of Mathematical Functions ID 18.15.E22

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \LaguerrepolyL[\alpha]{n}@{\nu x}=(-1)^{n}\frac{e^{\frac{1}{2}\nu x}}{2^{\alpha-\frac{1}{2}}x^{\frac{1}{2}\alpha+\frac{1}{4}}}\*\left(\frac{\zeta}{x-1}\right)^{\frac{1}{4}}\left(\frac{\AiryAi@{\nu^{\frac{2}{3}}\zeta}}{\nu^{\frac{1}{3}}}\sum_{m=0}^{M-1}\frac{E_{m}(\zeta)}{\nu^{2m}}+\frac{\AiryAi'@{\nu^{\frac{2}{3}}\zeta}}{\nu^{\frac{5}{3}}}\sum_{m=0}^{M-1}\frac{F_{m}(\zeta)}{\nu^{2m}}+\envAiryAi@{\nu^{\frac{2}{3}}\zeta}\bigO@{\frac{1}{\nu^{2M-\frac{2}{3}}}}\right),}

Symbols List

• ${\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}$:
• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle L^{(\NVar{\alpha})}_{\NVar{n}}\left(\NVar{x}\right)}}$: Laguerre (or generalized Laguerre) polynomial
• ${\displaystyle{\displaystyle\sim}}$:
• ${\displaystyle{\displaystyle\mathrm{envAi}\left(\NVar{x}\right)}}$:
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle m}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle\nu}}$: 18.15.E17
• ${\displaystyle{\displaystyle\zeta}}$: ζ
• ${\displaystyle{\displaystyle E_{m}}}$: coefficient
• ${\displaystyle{\displaystyle F_{m}}}$: coefficient (locally)
• ${\displaystyle{\displaystyle x}}$: real variable
 

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