Difference between revisions of "Bateman F"
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| − | The Bateman polynomials $F_n$ are defined by the formula | + | 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
- Harry Bateman: Some Properties of a certain Set of Polynomials (1933)... (previous)... (next) $3.$
- 1960: Earl David Rainville: Special Functions ... (previous) ... (next): $148. (1)$
