For all Integers and Nonnegative Integers , the harmonic logarithms of order and degree are defined as the unique functions satisfying

- 1. ,
- 2. has no constant term except ,
- 3. ,

(1) |

(2) | |||

(3) |

where is a Harmonic Number

(4) |

(5) |

(6) |

(7) |

(8) |

**References**

Loeb, D. and Rota, G.-C. ``Formal Power Series of Logarithmic Type.'' *Advances Math.* **75**, 1-118, 1989.

Roman, S. ``The Logarithmic Binomial Formula.'' *Amer. Math. Monthly* **99**, 641-648, 1992.

© 1996-9

1999-05-25