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,}}

0 references

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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