# Hypergeometric 0F1

From specialfunctionswiki

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)

# References

__Hypergeometric functions__