递归关系相关的勒让德多项式与施密特Semi-normalization -地球科学堆栈交换江南电子竞技平台江南体育网页版 最近30从www.hoelymoley.com 2023 - 08 - 05 - t11:21:35z //www.hoelymoley.com/feeds/question/20118 https://creativecommons.org/licenses/by-sa/4.0/rdf //www.hoelymoley.com/q/20118 2 递归关系的关联与施密特Semi-normalization勒让德多项式 Ayoub //www.hoelymoley.com/users/20950 2020 - 08 - 24 - t09:23:53z 2020 - 08 - 24 - t22:47:07z < p >谁能请提供我相关的勒让德多项式的递归关系当使用施密特quasi-normalization吗?我需要在地磁学的上下文中获取球面谐波系数g和h。< / p > //www.hoelymoley.com/questions/20118/-/20121 # 20121 2 回答WJB递归关系的关联与施密特Semi-normalization勒让德多项式 WJB //www.hoelymoley.com/users/14123 2020 - 08 - 24 - t14:51:06z 2020 - 08 - 24 - t22:47:07z < p >通知你,通常参考依赖地磁学中使用的方程是:< / p > < ul > <李> Langel, r。"Chapter four: Main field." Geomagnetism, edited by JA Jacobs (1987).

If it wasn't for lockdown I'd have copied from the book locked in my office to make sure I got it right...but until someone corrects me...

The Schmidt quasi/semi-normalisations for the associated Legendre polynomials are given by these recursions, in the form you'd actually use for calculations typically:

Note that if you use Schmidt normalisation of Legendre polynomials from a given software language to do calculations, you do not want to include the Condon-Shortley phase factor of . So check if it is included in the Legendre polynomial and/or normalisation formula.

Edit: Some links to open source geomagnetism compatible software for calculating Schmidt normalised associated Legendre polynomials.

Python: ChaosMagPy

Python/Fortran-95: SHTools
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