Formula:4584

Digital Library of Mathematical Functions ID 10.68.E17

${\displaystyle{\displaystyle\ln M_{\nu}\left(x\right)=\frac{x}{\sqrt{2}}-\frac{1}{2}\ln\left(2\pi x\right)-\frac{\mu-1}{8\sqrt{2}}\frac{1}{x}-\frac{(\mu-1)(\mu-25)}{384\sqrt{2}}\frac{1}{x^{3}}-\frac{(\mu-1)(\mu-13)}{128}\frac{1}{x^{4}}+O\left(\frac{1}{x^{5}}\right),}}$

Symbols List

• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle M_{\NVar{\nu}}\left(\NVar{x}\right)}}$: modulus of Bessel functions
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

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