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
Famous quotes containing the words functions, fractional and/or order:
“Adolescents, for all their self-involvement, are emerging from the self-centeredness of childhood. Their perception of other people has more depth. They are better equipped at appreciating others’ reasons for action, or the basis of others’ emotions. But this maturity functions in a piecemeal fashion. They show more understanding of their friends, but not of their teachers.”
—Terri Apter (20th century)
“Hummingbird
stay for a fractional sharp
sweetness, and’s gone, can’t take
more than that.”
—Denise Levertov (b. 1923)
“In Russia there is an emigration of intelligence: émigrés cross the frontier in order to read and to write good books. But in doing so they contribute to making their fatherland, abandoned by spirit, into the gaping jaws of Asia that would like to swallow our little Europe.”
—Friedrich Nietzsche (1844–1900)