Difference between revisions of "Bateman F"

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The Bateman polynomials $F_n$ are defined by the formula
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The Bateman polynomials $F_n$ are defined for $n=0,1,2,\ldots$ by the formula
 
$$F_n(z) = {}_3F_2 \left( -n, n+1, \dfrac{z+1}{2}; 1,1;1 \right),$$
 
$$F_n(z) = {}_3F_2 \left( -n, n+1, \dfrac{z+1}{2}; 1,1;1 \right),$$
 
where ${}_3F_2$ denotes the [[generalized hypergeometric function]].
 
where ${}_3F_2$ denotes the [[generalized hypergeometric function]].

Revision as of 05:47, 4 March 2018

The Bateman polynomials $F_n$ are defined for $n=0,1,2,\ldots$ by the formula $$F_n(z) = {}_3F_2 \left( -n, n+1, \dfrac{z+1}{2}; 1,1;1 \right),$$ where ${}_3F_2$ denotes the generalized hypergeometric function.

Properties

Generating relation for Bateman F
Three-term recurrence for Bateman F

References

Orthogonal polynomials