Difference between revisions of "Bessel polynomial"
From specialfunctionswiki
(Created page with "The Bessel polynomials are defined by $$y_n(x) = {}_2F_0 \left( -n, 1+n;-; -\dfrac{1}{2}x \right).$$") |
|||
| (8 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
| − | The Bessel polynomials are defined by | + | The Bessel polynomials are [[orthogonal polynomials]] defined by |
| − | $$y_n(x) = {} | + | $$y_n(x) = \displaystyle\sum_{k=0}^n \dfrac{(n+k)!}{(n-k)!k!} \left( \dfrac{x}{2} \right)^k.$$ |
| + | |||
| + | =Properties= | ||
| + | [[Bessel polynomial generalized hypergeometric]]<br /> | ||
| + | [[Bessel polynomial in terms of Bessel functions]]<br /> | ||
| + | [[Bessel at n+1/2 in terms of Bessel polynomial]]<br /> | ||
| + | [[Bessel at -n-1/2 in terms of Bessel polynomial]]<br /> | ||
| + | |||
| + | {{:Orthogonal polynomials footer}} | ||
| + | |||
| + | [[Category:SpecialFunction]] | ||
Latest revision as of 20:10, 9 June 2016
The Bessel polynomials are orthogonal polynomials defined by $$y_n(x) = \displaystyle\sum_{k=0}^n \dfrac{(n+k)!}{(n-k)!k!} \left( \dfrac{x}{2} \right)^k.$$
Properties
Bessel polynomial generalized hypergeometric
Bessel polynomial in terms of Bessel functions
Bessel at n+1/2 in terms of Bessel polynomial
Bessel at -n-1/2 in terms of Bessel polynomial
