Legendre Polynomials - Legendre Functions of Fractional Order

Legendre Functions of Fractional Order

Legendre functions of fractional order exist and follow from insertion of fractional derivatives as defined by fractional calculus and non-integer factorials (defined by the gamma function) into the Rodrigues' formula. The resulting functions continue to satisfy the Legendre differential equation throughout (−1,1), but are no longer regular at the endpoints. The fractional order Legendre function Pn agrees with the associated Legendre polynomial P0
n.

Read more about this topic:  Legendre Polynomials

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