DLMF:33.7.E3 (Q9540): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:33.7.E3	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle{H^{-}_{\ell}}\left(\eta,\rho\right)=\frac{-% \mathrm{i}e^{-\pi\eta}\rho^{\ell+1}}{(2\ell+1)!C_{\ell}\left(\eta\right)}\int_% {0}^{\infty}\left(\frac{\exp\left(-\mathrm{i}(\rho\tanh t-2\eta t)\right)}{(% \cosh t)^{2\ell+2}}+\mathrm{i}(1+t^{2})^{\ell}\exp\left(-\rho t+2\eta% \operatorname{arctan}t\right)\right)\mathrm{d}t,}}

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DLMF:33.7.E3

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normalizing constant for Coulomb radial functions

Defining formula

{\displaystyle{\displaystyle C_{\NVar{\ell}}\left(\NVar{\eta}\right)}}

C33.S2.E5.m2aadec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aadec

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Defining formula

{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

C1.S4.SS4.m1abdec

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exponential function

Defining formula

{\displaystyle{\displaystyle\exp\NVar{z}}}

C4.S2.E19.m2adec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2abdec

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Defining formula

{\displaystyle{\displaystyle!}}

introduction.Sx4.p1.t1.r15.m5aadec

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hyperbolic cosine function

Defining formula

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

C4.S28.E2.m2adec

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hyperbolic tangent function

Defining formula

{\displaystyle{\displaystyle\tanh\NVar{z}}}

C4.S28.E4.m2adec

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Defining formula

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

C1.S9.E1.m2abdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3abdec

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Defining formula

{\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}

C4.S23.SS2.p1.m7adec

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irregular Coulomb radial functions

Defining formula

{\displaystyle{\displaystyle{H^{\NVar{\pm}}_{\NVar{\ell}}}\left(\NVar{\eta},% \NVar{\rho}\right)}}

C33.S2.E7.m2aadec

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Defining formula

{\displaystyle{\displaystyle\ell}}

C33.S1.XMD2.m1bdec

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Defining formula

{\displaystyle{\displaystyle\rho}}

C33.S1.XMD5.m1bdec

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Defining formula

{\displaystyle{\displaystyle\eta}}

C33.S1.XMD7.m1bdec

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Sitelinks

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