Difference between revisions of "Bateman F"

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m (Tom moved page Bateman Z to Bateman F)
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The Bateman polynomials $Z_n$ are defined by the formula
+
The Bateman polynomials $F_n$ are defined by the formula
$$Z_n(x) = {}_2F_2(-n,n+1;1;1;x),$$
+
$$F_n(z) = {}_3F_2 \left( -n, n+1, \dfrac{z+1}{2}; 1,1;1 \right),$$
where ${}_2F_2$ is a [[generalized hypergeometric function]].
+
where ${}_3F_2$ is a [[generalized hypergeometric function]].
  
 
=Properties=
 
=Properties=

Revision as of 02:13, 22 June 2016

The Bateman polynomials $F_n$ are defined by the formula $$F_n(z) = {}_3F_2 \left( -n, n+1, \dfrac{z+1}{2}; 1,1;1 \right),$$ where ${}_3F_2$ is a generalized hypergeometric function.

Properties

References

Orthogonal polynomials