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In mathematics, the local Heun function Hℓ(a,q;α,β,γ,δ;z) is the solution of Heun's differential equation that is holomorphic and 1 at the singular point ''z'' = 0. The local Heun function is called a Heun function, denoted ''Hf'', if it is also regular at ''z'' = 1, and is called a Heun polynomial, denoted ''Hp'', if it is regular at all three finite singular points ''z'' = 0, 1, ''a''. ==Heun's equation== Heun's equation is a second-order linear ordinary differential equation (ODE) of the form : The condition is needed to ensure regularity of the point at ∞. The complex number ''q'' is called the accessory parameter. Heun's equation has four regular singular points: 0, 1, ''a'' and ∞ with exponents (0, 1 − γ), (0, 1 − δ), (0, 1 − ϵ), and (α, β). Every second-order linear ODE on the extended complex plane with at most four regular singular points, such as the Lamé equation or the hypergeometric differential equation, can be transformed into this equation by a change of variable. 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「Heun function」の詳細全文を読む スポンサード リンク
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