Consider the ODE [itex] [/itex] [itex]y''+P(x)y'+Q(x)y=0[/itex].(adsbygoogle = window.adsbygoogle || []).push({});

If [itex]\stackrel{limit}{_{x→x_{o}}}P(x)[/itex] and [itex]\stackrel{limit}{_{x→x_{o}}}Q(x)[/itex] converge, can you call [itex]x_{o}[/itex] a 'regular singular point' besides calling it an 'ordinary point'?

I am saying this because if [itex]\stackrel{limit}{_{x→x_{o}}}P(x)[/itex] and [itex]\stackrel{limit}{_{x→x_{o}}}Q(x)[/itex] converge, then [itex]\stackrel{limit}{_{x→x_{o}}}(x-x_{o})P(x)[/itex] and [itex]\stackrel{limit}{_{x→x_{o}}}(x-x_{o})^{2}Q(x)[/itex] will also converge. And for a second-order linear ODE for which [itex]\stackrel{limit}{_{x→x_{o}}}(x-x_{o})P(x)[/itex] and [itex]\stackrel{limit}{_{x→x_{o}}}(x-x_{o})^{2}Q(x)[/itex] converge, [itex]x_{o}[/itex] is termed as a regular singular point.

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Isn't Ordinary Point Just a Specific Case of Regular Singular Point?

Loading...

Similar Threads - Isn't Ordinary Point | Date |
---|---|

I How to find a solution to this linear ODE? | Feb 21, 2018 |

A How to simplify the solution of the following linear homogeneous ODE? | Feb 18, 2018 |

I Two point boundary problem - Shooting method | May 26, 2017 |

A Solution of ODEs With the Method of Iterated Integrals | Jan 8, 2017 |

Special Second Order Ordinary Diff. Equation | Jan 26, 2016 |

**Physics Forums - The Fusion of Science and Community**