]> $${}_0{F}_1\left(;b;z\right)=1+\frac{z}{b\left(1+K_k{\left(-\frac{z}{\left(k+1\right)\left(b+k\right)},\frac{z}{\left(k+1\right)\left(b+k\right)}+1\right)}_1^{\infty }\right)}$$