Abstract
The Legendre polynomial of degree l (l = 0,1,2,..., ∞) is defined by the formula
(C.1) It is a polynomial with l zeros in the range (−1, +1) and with parity (− 1)l. The first five Legendre polynomials are P 0 = 1, (C.2) P 1 = u, (C.3) P 2 = 1/2(3u 2-1), (C.4) P 3 = 1/2(5u 3−3u), (C.5) P 4 = 1/8 (35u 4 − 30u 2 + 3). (C.6)
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© 2003 Springer-Verlag Berlin Heidelberg
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(2003). Special Functions. In: Dapor, M. (eds) Electron-Beam Interactions with Solids. Springer Tracts in Modern Physics, vol 186. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36507-9_9
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DOI: https://doi.org/10.1007/3-540-36507-9_9
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