Formula:4450

Digital Library of Mathematical Functions ID 10.52.E5

${\displaystyle{\displaystyle{\mathsf{i}^{(1)}_{n}}\left(z\right)\sim{\mathsf{i}^{(2)}_{n}}\left(z\right)\sim\tfrac{1}{2}z^{-1}e^{z},}}$

Constraint(s)

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

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
• ${\displaystyle{\displaystyle\operatorname{ph}}}$: phase
• ${\displaystyle{\displaystyle{\mathsf{i}^{(1)}_{\NVar{n}}}\left(\NVar{z}\right)}}$: modified spherical Bessel function
• ${\displaystyle{\displaystyle{\mathsf{i}^{(2)}_{\NVar{n}}}\left(\NVar{z}\right)}}$: modified spherical Bessel function
• ${\displaystyle{\displaystyle n}}$: integer
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\delta}}$: small positive constant
 

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