# Fn fn 1 fn 2

Input |
---|

(f n) (f n)×1 (f n)×2 |

Result |

2 f^3 n^3 |

Values |

f | 0 | 0 1 | 2 n^3 2 | 16 n^3 3 | 54 n^3 |

Plots |

f | 0 | 1 | 2 | 3 | |

Polynomial discriminant |

Delta = 0 |

Property as a function |

odd |

Derivative |

(d)/(dn)((f n) (f n) (f n)×2) = 6 f^3 n^2 |

Indefinite integral |

integral 2 f^3 n^3 dn = (f^3 n^4)/2 + constant |

Definite integral over a square of edge length 2 L |

integral_(-L)^L integral_(-L)^L 2 f^3 n^3 dn df = 0 |