Generalizations of Wilson’s Theorem for Double-, Hyper-, Sub- and Superfactorials

@article{Aebi2015GeneralizationsOW,
  title={Generalizations of Wilson’s Theorem for Double-, Hyper-, Sub- and Superfactorials},
  author={Christian Aebi and Grant Cairns},
  journal={The American Mathematical Monthly},
  year={2015},
  volume={122},
  pages={433 - 443}
}
Abstract We present generalizations of Wilson’s theorem for double factorials, hyperfactorials, subfactorials, and superfactorials. 
Jacobi-Type Continued Fractions for the Ordinary Generating Functions of Generalized Factorial Functions
TLDR
The article serves as a semi-comprehensive, detailed survey reference that introduces applications to many established and otherwise well-known combinatorial identities, new cases of generating functions for factorial-function-related product sequences, and other examples of the generalized integer-valued multifactorial, or $\alpha$-factorial, function sequences.

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