Polynomials
that can be defined by the sum
|
(1)
|
for ,
where
is the floor function. They obey the recurrence
relation
|
(2)
|
for .
They have the integral representation
|
(3)
|
and the generating function
|
(4)
|
(Gradshteyn and Ryzhik 2000, p. 990), and obey the Neumann
differential equation.
The first few Neumann polynomials are given by
(OEIS A057869).
See also
Neumann Differential
Equation,
Schläfli Polynomial
Explore with Wolfram|Alpha
References
Erdelyi, A.; Magnus, W.; Oberhettinger, F.; and Tricomi, F. G. Higher
Transcendental Functions, Vol. 2. Krieger, pp. 32-33, 1981.Gradshteyn,
I. S. and Ryzhik, I. M. "Neumann's and Schläfli Polynomials:
and ."
§8.59 in Tables
of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press,
pp. 989-991, 2000.Sloane, N. J. A. Sequence A057869
in "The On-Line Encyclopedia of Integer Sequences."von Seggern,
D. CRC
Standard Curves and Surfaces. Boca Raton, FL: CRC Press, p. 196, 1993.Watson,
G. N. A
Treatise on the Theory of Bessel Functions, 2nd ed. Cambridge, England: Cambridge
University Press, pp. 298-305, 1966.Referenced on Wolfram|Alpha
Neumann Polynomial
Cite this as:
Weisstein, Eric W. "Neumann Polynomial."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NeumannPolynomial.html
Subject classifications