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

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, .'' Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 701-707, 1985.

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 and .'' Ch. 59 in An Atlas of Functions. Washington, DC: Hemisphere, pp. 581-597, 1987.

• Unicursal Circuit
• Uniform Apodization Function
• Uniform Boundedness Principle
• Uniform Convergence
• Uniform Distribution
• Uniform Polyhedron
• Uniform Variate
• Unimodal Distribution
• Unimodal Sequence
• Unimodular Group
• Unimodular Matrix
• Unimodular Transformation
• Union
• Uniplanar Double Point
• Unipotent
• Unique
• Unique Factorization Theorem
• Unit
• Unital
• Unitary Aliquot Sequence
• Unitary Amicable Pair
• Unitary Divisor
• Unitary Group
• Unitary Matrix
• Unitary Multiperfect Number