米塔-列夫勒函数

对应 ${\displaystyle a=0,1/2,1,2}$ 有

${\displaystyle E_{0,1}(z)=\sum _{k=0}^{\infty }z^{k}={\frac {1}{1-z}}.}$

指数函数:

${\displaystyle E_{1,1}(z)=\sum _{k=0}^{\infty }{\frac {z^{k}}{\Gamma (k+1)}}=\sum _{k=0}^{\infty }{\frac {z^{k}}{k!}}=\exp(z).}$

误差函数:

${\displaystyle E_{1/2,1}(z)=\exp(z^{2})\operatorname {erfc} (-z).}$

双曲余弦:

${\displaystyle E_{2,1}(z)=\cosh({\sqrt {z}}).}$

对应 ${\displaystyle a=0,1,2}$, ：

${\displaystyle \int _{0}^{z}E_{\alpha ,1}(-s^{2}){\mathrm {d} }s}$ 有下列积分式

${\displaystyle \arctan(z)}$,

${\displaystyle {\tfrac {\sqrt {\pi }}{2}}\operatorname {erf} (z)}$,

${\displaystyle \sin(z)}$.

• Mittag-Leffler, M.G.: Sur la nouvelle fonction E(x). C. R. Acad. Sci. Paris 137, 554–558 (1903)
• Mittag-Leffler, M.G.: Sopra la funzione E˛.x/. Rend. R. Acc. Lincei, (Ser. 5) 13, 3–5 (1904)
• Gorenflo R., Kilbas A.A., Mainardi F., Rogosin S.V., Mittag-Leffler Functions, Related Topics and Applications (Springer, New York, 2014) 443 pages ISBN 978-3-662-43929-6

• Olver, F. W. J.; Maximon, L. C., , Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W. (编), , Cambridge University Press, 2010, ISBN 978-0521192255, MR2723248
• Igor Podlubny. . . Mathematics in Science and Engineering. Academic Press. 1998. ISBN 0-12-558840-2.
• Kai Diethelm. . . Lecture notes in mathematics. Heidelberg and New York: Springer-Verlag. 2010. ISBN 978-3-642-14573-5.