Formula:4214

Digital Library of Mathematical Functions ID 10.30.E5

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \modBesselI{\nu}@{z}\asympeq e^{\pm(\nu+\frac{1}{2})\pi i}e^{-z}/\sqrt{2\pi z},}

Constraint(s)

${\displaystyle{\displaystyle\tfrac{1}{2}\pi+\delta\leq\pm\operatorname{ph}z\leq\tfrac{3}{2}\pi-\delta}}$

Symbols List

• ${\displaystyle{\displaystyle\sim}}$: asymptotic equality
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}$: modified Bessel function of the first kind
• ${\displaystyle{\displaystyle\operatorname{ph}}}$: phase
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
• ${\displaystyle{\displaystyle\delta}}$: small positive constant
 

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