I am just reading about mittag leffler function and its properties :
The hyperbolic functions of order n .which are generalizations of the hyperbolic sine and cosine can be expressed in terms of mittag -leffler function:
$ {h}_{r}{\mathrm{(}}{z}{\mathrm{,}}{n}{\mathrm{)}}\mathrm{{=}}\mathop{\sum}\limits_{{k}\mathrm{{=}}{0}}\limits^{\mathrm{\infty}}{\frac{{z}^{{nk}\mathrm{{+}}{r}\mathrm{{-}}{1}}}{{\mathrm{(}}{nk}\mathrm{{+}}{r}\mathrm{{-}}{1}{\mathrm{)}}}}\mathrm{{=}}{z}^{{r}\mathrm{{-}}{1}}{E}_{n\mathrm{,}r}{\mathrm{(}}{z}^{n}{\mathrm{).}}\hspace{0.33em}\hspace{0.33em}{\mathrm{(}}{r}\mathrm{{=}}{1}{\mathrm{,}}{2}{\mathrm{,...}}{n}{\mathrm{)}} $
Is there any explanation for that relationship .