# generalized Ruiz’s identity

For $i,j=1,2,\mathrm{\dots}$, consider the polynomials^{} ${c}_{i,j}(x)={(x+i)}^{j}-{(x+i-1)}^{j}$ ($x$ is the indeterminate^{}). Then, for every positive natural number $n$,

$$det{({c}_{i,j})}_{i,j=1}^{n}=\prod _{k=1}^{n}k!$$ |

Title | generalized Ruiz’s identity^{} |
---|---|

Canonical name | GeneralizedRuizsIdentity |

Date of creation | 2013-03-22 14:31:45 |

Last modified on | 2013-03-22 14:31:45 |

Owner | GeraW (6138) |

Last modified by | GeraW (6138) |

Numerical id | 7 |

Author | GeraW (6138) |

Entry type | Derivation |

Classification | msc 11B65 |

Classification | msc 05A10 |

Related topic | determinant2 |

Related topic | Determinant2 |