DLMF:28.20.E11 (Q8343)

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Language	Label	Description	Also known as
English	DLMF:28.20.E11	No description defined

Statements

Defining formula

{\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),}}

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DLMF:28.20.E11

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Bessel function of the first kind

Defining formula

{\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}

C10.S2.E2.m2adec

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order not exceeding

Defining formula

{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}

C2.S1.E3.m2abdec

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base of natural logarithm

Defining formula

{\displaystyle{\displaystyle\mathrm{e}}}

C4.S2.E11.m2adec

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hyperbolic cosine function

Defining formula

{\displaystyle{\displaystyle\cosh\NVar{z}}}

C4.S28.E2.m2addec

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hyperbolic secant function

Defining formula

{\displaystyle{\displaystyle\operatorname{sech}\NVar{z}}}

C4.S28.E6.m2abdec

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Defining formula

{\displaystyle{\displaystyle\Im}}

C1.S9.E2.m2adec

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Defining formula

{\displaystyle{\displaystyle{\mathrm{M}^{(\NVar{j})}_{\NVar{\nu}}}\left(\NVar{% z},\NVar{h}\right)}}

C28.S20.SS3.p1.m4abdec

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Defining formula

{\displaystyle{\displaystyle h}}

C28.S1.XMD11.m1cdec

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Defining formula

{\displaystyle{\displaystyle z}}

C28.S1.XMD6.m1idec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C28.S1.XMD7.m1edec

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