DLMF:10.47.E13 (Q3683)

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Language	Label	Description	Also known as
English	DLMF:10.47.E13	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\mathsf{k}_{n}\left(z\right)=-\tfrac{1}{2}\pi i^{n% }{\mathsf{h}^{(1)}_{n}}\left(iz\right)=-\tfrac{1}{2}\pi i^{-n}{\mathsf{h}^{(2)% }_{n}}\left(-iz\right).}}

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DLMF:10.47.E13

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2ahdec

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Defining formula

{\displaystyle{\displaystyle\mathrm{i}}}

C1.S9.E1.m2addec

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modified spherical Bessel function

Defining formula

{\displaystyle{\displaystyle\mathsf{k}_{\NVar{n}}\left(\NVar{z}\right)}}

C10.S47.E9.m2abdec

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spherical Bessel function of the third kind

Defining formula

{\displaystyle{\displaystyle{\mathsf{h}^{(1)}_{\NVar{n}}}\left(\NVar{z}\right)}}

C10.S47.E5.m2abdec

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spherical Bessel function of the third kind

Defining formula

{\displaystyle{\displaystyle{\mathsf{h}^{(2)}_{\NVar{n}}}\left(\NVar{z}\right)}}

C10.S47.E6.m2abdec

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