mittlefferr(α,β,z,ρ) # evaluate Mittag-Leffler function with tolerance ρ
mittlefferr(α,z,ρ) # mittlefferr(α,1,z,ρ)
mittleff(α,β,z) # evaluate Mittag-Leffler function with tolerance eps()
mittleff(α,z) # mittleff(α,1,z)
Arguments must satisfy α > 0
, β
real, z
real or complex, ρ>0
.
For α<1
and/or abs(z)<1
, accurate, series-only method are used. The series-only methods work
with BigFloat precision for corresponding input types. Some other parameter ranges also use series
or asymptotic methods.
For some arguments, integrals are evaluated with quadgk
, with no control on errors. Some results
are accurate, others are not.
mittleffderiv(α,β,z) # evaluate derivative of Mittag-Leffler function
mittleffderiv(α,z) # mittleffderiv(α,1,z)
mittleff
fails for some arguments. In particular, some of those that evaluate integrals.
Rudolfo Gorenflo, Joulia Loutchko and Yuri Loutchko, Computation of the Mittag-Leffler function and its derivative, Fract. Calc. Appl. Anal, (2002)