An extension of the -function

(1) |

(2) |

(3) |

The -function is given by the integral

(4) |

(5) |

(6) |

(7) |

(8) | |||

(9) | |||

(10) |

and is the Euler-Mascheroni Constant (Gosper).

The first few values of for , 3, ... are 1, 4, 108, 27648, 86400000, 4031078400000, ... (Sloane's A002109). These numbers are called Hyperfactorials by Sloane and Plouffe (1995).

**References**

Sloane, N. J. A. Sequence
A002109/M3706
in ``An On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.
*The Encyclopedia of Integer Sequences.* San Diego: Academic Press, 1995.

© 1996-9

1999-05-26