查看“︁库伦函数”︁的源代码

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[[File:Coulomb F function plot.png|thumb|Coulomb F function plot]]
[[File:Coulomb G function plot.png|thumb|Coulomb  G  function plot]]
'''库伦函数'''(Couloumb function)是下列常微分方程的解

<math>\frac{d^2w(\rho)}{d\rho^2}+(1-\frac{2\eta}{\rho}-\frac{l*(l+1)}{\rho^2})*w(\rho)=0</math>

此方程的两个解为：

<math>F_\ell(\eta,\rho)</math> 和 <math>G_\ell(\eta,\rho)</math>, 以 [[合流超几何函数]]表示<ref>{{dlmf|first=I. J.|last=Thompson|id=33|title=Coulomb Functions}}</ref><ref>{{AS ref |14|538}}</ref>
:<math>F_\ell(\eta,\rho) = \frac{2^\ell e^{-\pi\eta/2}|\Gamma(\ell+1+i\eta)|}{(2\ell+1)!}\rho^{\ell+1}e^{\mp i\rho}M(\ell+1\mp i\eta,2\ell+2,\pm 2i\rho) \,.</math>


==参考文献==
<references/>

*{{citation|first=Harry|last=Bateman|title=Higher transcendental functions|volume=1|year=1953|publisher=McGraw-Hill|url=http://apps.nrbook.com/bateman/Vol1.pdf|accessdate=2015-02-11|archive-date=2011-08-11|archive-url=https://web.archive.org/web/20110811153220/http://apps.nrbook.com/bateman/Vol1.pdf|dead-url=no}}.
*{{Citation | last1=Jaeger | first1=J. C. | last2=Hulme | first2=H. R. | title=The Internal Conversion of γ -Rays with the Production of Electrons and Positrons | jstor=96298 | publisher=The Royal Society | year=1935 | journal=Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences | issn=0080-4630 | volume=148 | issue=865 | pages=708–728 | doi=10.1098/rspa.1935.0043|bibcode = 1935RSPSA.148..708J }}
*{{Citation | last1=Slater | first1=Lucy Joan | title=Confluent hypergeometric functions | publisher=[[Cambridge University Press]] | mr=0107026 | year=1960}}.



[[Category:特殊函数]]