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:
“Empirical science is apt to cloud the sight, and, by the very knowledge of functions and processes, to bereave the student of the manly contemplation of the whole.”
—Ralph Waldo Emerson (1803–1882)
“Hummingbird
stay for a fractional sharp
sweetness, and’s gone, can’t take
more than that.”
—Denise Levertov (b. 1923)
“When the book comes out it may hurt you—but in order for me to do it, it had to hurt me first. I can only tell you about yourself as much as I can face about myself.”
—James Baldwin (1924–1987)