DLMF:28.20.E11

MaRDI QIDQ9036

• Label: DLMF:28.20.E11

Digital Library of Mathematical Functions ID 28.20.E11

${\displaystyle{\displaystyle{\mathrm{M}^{(1)}_{\nu}}\left(z,h\right)=J_{\nu}\left(2h\cosh z\right)+e^{|\Im(2h\cosh z)|}O\left(\left(\operatorname{sech}z\right)^{3/2}\right),}}$

Symbols List

• ${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Bessel function of the first kind
• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\cosh\NVar{z}}}$: hyperbolic cosine function
• ${\displaystyle{\displaystyle\operatorname{sech}\NVar{z}}}$: hyperbolic secant function
• ${\displaystyle{\displaystyle\Im}}$: imaginary part
• ${\displaystyle{\displaystyle{\mathrm{M}^{(\NVar{j})}_{\NVar{\nu}}}\left(\NVar{z},\NVar{h}\right)}}$:
• ${\displaystyle{\displaystyle h}}$: parameter
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

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