In this article, an operational definition, generating function, explicit summation formula, determinant definition and recurrence relations of the generalized families of Hermite–Appell polynomials are derived by using integral transforms and some known operational rules. An analogous study of these results is also carried out for the generalized forms of the Hermite–Bernoulli and Hermite–Euler polynomials.

中文翻译：

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与Appell序列相关的分数阶微积分和特殊多项式的广义形式

在本文中，通过使用积分变换和一些已知的运算规则，得出了Hermite-Appell多项式广义族的运算定义，生成函数，显式求和公式，行列式定义和递归关系。还针对Hermite-Bernoulli和Hermite-Euler多项式的广义形式对这些结果进行了类似的研究。