%0 Journal Article %T Second Hankel determinant for a class defined by modified Mittag-Leffler with generalized polylogarithm functions %A Pauzi, M. N. M. %A Darus, M. %A Siregar, S. %J Journal of Mathematics and Computer Science %D 2018 %V 18 %N 4 %@ ISSN 2008-949X %F Pauzi2018 %X In this work, a new generalized derivative operator \( \mathfrak{M}_{\alpha,\beta,\lambda}^{m}\) is introduced. This operator obtained by using convolution (or Hadamard product) between the linear operator of the generalized Mittag-Leffler function in terms of the extensively-investigated Fox-Wright \(_{p}\Psi_{q}\) function and generalized polylogarithm functions defined by \[ \mathfrak{M}_{\alpha,\beta,\lambda}^{m}f(z)=\mathfrak{F}_{\alpha,\beta}f(z)*\mathfrak{D}_{\lambda}^{m}f(z) = z+\sum_{n=2}^{\infty}\frac{\Gamma(\beta)n^{m}(n+\lambda-1)!}{\Gamma[\alpha(n-1)+\beta]\lambda ! (n-1)!}a_{n}z^{n}, \] where \(m \in \mathbb{N}_{0} = \{0,1,2,3,\ldots\}\) and \(\min\{Re(\alpha),Re(\beta)\}>0\). By making use of \(\mathfrak{M}_{\alpha,\beta,\lambda}^{m}f(z)\), a class of analytic functions is introduced. The sharp upper bound for the nonlinear \(|a_{2}a_{4}-a_{3}^{2}|\) (also called the second Hankel functional) is obtained. Relevant connections of the results presented here with those given in earlier works are also indicated. %9 journal article %R 10.22436/jmcs.018.04.06 %U http://dx.doi.org/10.22436/jmcs.018.04.06 %P 453--459