Legendre Function of the Second Kind
A solution to the Legendre Differential Equation which is singular at the origin. The Legendre functions of thesecond kind satisfy the same Recurrence Relation as the Legendre Functions of the First Kind. The first few are
The associated Legendre functions of the second kind have Derivative about 0 of
(Abramowitz and Stegun 1972, p. 334). The logarithmic derivative is
(Binney and Tremaine 1987, p. 654).
References
Abramowitz, M. and Stegun, C. A. (Eds.). ``Legendre Functions.'' Ch. 8 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 331-339, 1972. Arfken, G. ``Legendre Functions of the Second Kind, Binney, J. and Tremaine, S. ``Associated Legendre Functions.'' Appendix 5 in Galactic Dynamics. Princeton, NJ: Princeton University Press, pp. 654-655, 1987. Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 597-600, 1953. Snow, C. Hypergeometric and Legendre Functions with Applications to Integral Equations of Potential Theory. Washington, DC: U. S. Government Printing Office, 1952. Spanier, J. and Oldham, K. B. ``The Legendre Functions 
.'' Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 701-707, 1985.
and 
.'' Ch. 59 in An Atlas of Functions. Washington, DC: Hemisphere, pp. 581-597, 1987.
- U-Number
- Upper Bound
- Upper Integral
- Upper Limit
- Upper Sum
- Upper-Trimmed Subsequence
- Upward Drawing
- Urchin
- Utility Graph
- Utility Problem
- Valence
- Valency
- Valuation
- Valuation Group
- Valuation Ring
- Valuation Theory
- Value
- Value (Game)
- Vampire Number
- van der Grinten Projection
- Vandermonde Determinant
- Vandermonde Identity
- Vandermonde Matrix
- Vandermonde's Sum
- Vandermonde Theorem