Mittag-Leffler Function

$$E_\gamma(x)\equiv\sum_{k=0}^\infty {x^k\over\Gamma(\gamma k+1)}.$$

It is related to the Generalized Hyperbolic Functions by

$$F_{n,0}^1(x)=E_n(x^n).$$

References

Muldoon, M. E. and Ungar, A. A. ``Beyond Sin and Cos.'' Math. Mag. 69, 3-14, 1996.