Formula:10288

Digital Library of Mathematical Functions ID 33.12.E2

${\displaystyle{\displaystyle{F_{0}\left(\eta,\rho\right)\atop G_{0}\left(\eta,\rho\right)}\sim\pi^{1/2}(2\eta)^{1/6}\left\{{\mathrm{Ai}\left(x\right)\atop\mathrm{Bi}\left(x\right)}\left(1+\frac{B_{1}}{\mu}+\frac{B_{2}}{\mu^{2}}+\cdots\right)+{\mathrm{Ai}'\left(x\right)\atop\mathrm{Bi}'\left(x\right)}\left(\frac{A_{1}}{\mu}+\frac{A_{2}}{\mu^{2}}+\cdots\right)\right\},}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}$:
• ${\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}$:
• ${\displaystyle{\displaystyle\sim}}$:
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle G_{\NVar{\ell}}\left(\NVar{\eta},\NVar{\rho}\right)}}$: irregular Coulomb radial function
• ${\displaystyle{\displaystyle F_{\NVar{\ell}}\left(\NVar{\eta},\NVar{\rho}\right)}}$: regular Coulomb radial function
• ${\displaystyle{\displaystyle\rho}}$: nonnegative real variable
• ${\displaystyle{\displaystyle\eta}}$: real parameter
• ${\displaystyle{\displaystyle x}}$: variable
• ${\displaystyle{\displaystyle\mu}}$: variable
• ${\displaystyle{\displaystyle A_{j}}}$: coefficients
• ${\displaystyle{\displaystyle B_{j}}}$: coefficients
 

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