Difference between revisions of "Hypergeometric 0F1"
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[[Relationship between Bessel-Clifford and hypergeometric 0F1]]<br /> | [[Relationship between Bessel-Clifford and hypergeometric 0F1]]<br /> | ||
[[0F1(;r;z)0F1(;s;z)=2F1(r/2+s/2, r/2+s/2-1/2;r,s,r+s-1;4z)]]<br /> | [[0F1(;r;z)0F1(;s;z)=2F1(r/2+s/2, r/2+s/2-1/2;r,s,r+s-1;4z)]]<br /> | ||
| + | [[0F1(;r;z)0F1(;r;-z)=0F3(r,r/2,r/2+1/2;-z^2/4)]]<br /> | ||
=References= | =References= | ||
Latest revision as of 20:22, 17 June 2017
The hypergeometric ${}_0F_1$ is defined by the series $${}_0F_1(;a;z)=\displaystyle\sum_{k=0}^{\infty} \dfrac{z^k}{(a)_k k!},$$ where $(a)_k$ denotes the Pochhammer symbol and $k!$ denotes the factorial.
Properties
Relationship between cosine and hypergeometric 0F1
Relationship between sine and hypergeometric 0F1
Relationship between cosh and hypergeometric 0F1
Relationship between sinh and hypergeometric 0F1
Relationship between Bessel J sub nu and hypergeometric 0F1
Relationship between Bessel-Clifford and hypergeometric 0F1
0F1(;r;z)0F1(;s;z)=2F1(r/2+s/2, r/2+s/2-1/2;r,s,r+s-1;4z)
0F1(;r;z)0F1(;r;-z)=0F3(r,r/2,r/2+1/2;-z^2/4)
