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172 SPHERICAL HAKMONICS.
r, wl (ya mere)
ebe J^-) na-egosi uru Y i na nha nhata (27) n'otu ntabi anya okporo osisi nile nke Qj.
140.] N'ihi nke a bụ ihe dị ezigbo mkpa na tiori nke spherical harmonics, dị ka ọ na-eduga ná mkpebi siri ike nke ụdị nke usoro nke sppherical harmonics, nke na-egosipụta ọrụ nwere uru ọ bụla ekenyere aka ike n'ókè nke ọ bụla nke elu okirikiri.
Maka ka F bụrụ uru nke ọrụ ahụ n'ebe ọ bụla e nyere Sphere, kwuo n'etiti ike ndọda nke mmewere nke elu dS, ka Q bụrụkwa zonal harmonic nke ogo m onye ogwe aka ya bụ isi P na sphere, mgbe ahụ elu-integral
gbatịa n'elu okirikiri okirikiri ga-abụ harmonic okirikiri nke ogo m, n'ihi na ọ bụ nchikota nke ọtụtụ zonal harmonics onye mkpanaka ya bụ ihe dị iche iche dS, nke ọ bụla na-amụba ya FdS. N'ihi ya, ọ bụrụ na anyị na-eme
anyị nwere ike ịgbasa F n'ụdị
F= AJo + A^ + bc. + AịYị, (62)
ma ọ bụ
1
471 a*
. (63)
Nke a bụ usoro Laplace a na-eme ememme maka mgbasawanye na
usoro harmonics okirikiri nke ọ bụla ekesara n'elu
elu nke okirikiri. N'iji ya eme ihe, anyị kwesịrị iji
were otu isi ihe P na okirikiri dị ka okporo osisi nke zonal
harmonic Q {, na ịchọta elu-integral
n'elu dum elu nke sphere. Nsonaazụ nke ọrụ a
mgbe mụbaa site na 2i+I na-enye uru nke A i Y i n'ebe P.
na site n'ime ka P na-eme njem n'elu elu nke gburugburu uru nke
Enwere ike ịchọta A {Y { n'ebe ọ bụla ọzọ.
