Formula:4276

Digital Library of Mathematical Functions ID 10.40.E1

${\displaystyle{\displaystyle I_{\nu}\left(z\right)\sim\frac{e^{z}}{(2\pi z)^{\frac{1}{2}}}\sum_{k=0}^{\infty}(-1)^{k}\frac{a_{k}(\nu)}{z^{k}},}}$

Constraint(s)

${\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{1}{2}\pi-\delta}}$

Symbols List

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

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