第二类椭球谐波，也称为第二类拉梅函数，有多种定义方式，如下：
![F_m^p(x)=(2m+1)E_m^p(x)int_x^infty(dx)/(sqrt((x^2-b^2)(x^2-c^2))[E_m^p(x)]^2)](/images/equations/EllipsoidalHarmonicoftheSecondKind/NumberedEquation1.svg) |
(Byerly 1959, p. 258) 或
![F_m^p(x)=(2m+1)E_m^p(x)int_0^u(du)/([E_m^p(u)]^2)](/images/equations/EllipsoidalHarmonicoftheSecondKind/NumberedEquation2.svg) |
(Heine 1845, p. 194; Whittaker and Watson 1990, p. 562)。
第二类椭球谐波
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参考文献
Byerly, W. E. "Laplace's Equation in Curvilinear Coördinates. Ellipsoidal Harmonics." 章 8 in An Elementary Treatise on Fourier's Series, and Spherical, Cylindrical, and Ellipsoidal Harmonics, with Applications to Problems in Mathematical Physics. New York: Dover, 页 251-266, 1959.Heine, E. "Beitrag zur Theorie der Anziehung und der Wärme." J. reine angew. Math. 29, 185-208, 1845.Whittaker, E. T. and Watson, G. N. "Lamé Functions of the Second Kind." §23.47 in A Course in Modern Analysis, 4th ed. Cambridge, England: Cambridge University Press, 页 562-563, 1990.在 中被引用
第二类椭球谐波请引用为
Weisstein, Eric W. "第二类椭球谐波。" 来自 --一个 Wolfram 网络资源。 https://mathworld.net.cn/EllipsoidalHarmonicoftheSecondKind.html