Heun function

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In mathematics, the local Heun function ${\displaystyle H\ell (a,q;\alpha ,\beta ,\gamma ,\delta ;z)}$ (Karl L. W. Heun 1889) 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.