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In mathematics, the Legendre functions ''P''λ, ''Q''λ and associated Legendre functions ''P'', ''Q'' are generalizations of Legendre polynomials to non-integer degree. ==Differential equation== Associated Legendre functions are solutions of the general Legendre equation : where the complex numbers λ and μ are called the degree and order of the associated Legendre functions, respectively. The Legendre polynomials are the associated Legendre functions of order μ=0. This is a second order linear equation with three regular singular points (at 1, −1, and ∞). Like all such equations, it can be converted into a hypergeometric differential equation by a change of variable, and its solutions can be expressed using hypergeometric functions. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Legendre function」の詳細全文を読む スポンサード リンク
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