Message boards : Science (non-SETI) : Non-integer factorials?

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Sergej O. S. Volunteer tester Send message Joined: 29 Oct 08 Posts: 123 Credit: 44,886 RAC: 0 | |

Hi. I'm writing a program (as one of my hobbies) that calculates factorials. But people are telling me that non-integer factorials have no use - the Gamma function instead - G(z)=(z-1)!. | |

ID: 824881 · | |

William Rothamel Send message Joined: 25 Oct 06 Posts: 3226 Credit: 1,265,766 RAC: 322 | |

My intuition tells me that rational, non-integer factorials would be useful in determining series convergences--albeit with some fiddling with scale factors. | |

ID: 824914 · | |

Clyde C. Phillips, III Send message Joined: 2 Aug 00 Posts: 1851 Credit: 5,955,047 RAC: 0 | |

So, what is 2.5!? 1 x 2 x (3)^1/2? Probably not, because that last factor is probably calculated by a different rule. Maybe non-integer factorials never have been defined. | |

ID: 824961 · | |

Sergej O. S. Volunteer tester Send message Joined: 29 Oct 08 Posts: 123 Credit: 44,886 RAC: 0 | |

My intuition tells me that rational, non-integer factorials would be useful in determining series convergences--albeit with some fiddling with scale factors. Thank you. I'll try to find the formula for practical use on that field... | |

ID: 824977 · | |

Sergej O. S. Volunteer tester Send message Joined: 29 Oct 08 Posts: 123 Credit: 44,886 RAC: 0 | |

So, what is 2.5!? 1 x 2 x (3)^1/2? Probably not, because that last factor is probably calculated by a different rule. Maybe non-integer factorials never have been defined. Is 96% true. Exactly, 2.5! = 0.5 * 1.5 * 2.5 * pi^0.5 Unfortunately, values other than integer + 0.5 doesn't work that way, or I don't see how... | |

ID: 824979 · | |

HTH Volunteer tester Send message Joined: 8 Jul 00 Posts: 690 Credit: 845,606 RAC: 345 | |

Hi. I'm writing a program (as one of my hobbies) that calculates factorials. But people are telling me that non-integer factorials have no use - the Gamma function instead - G(z)=(z-1)!. The gamma function is the generalization of the factorial function. Some gadgets and formulas: [tex] n! = \Gamma(n+1) \Gamma(p) = \int_{0}^{\infty}e^{-x}x^{p-1}\,\text{d}x \Gamma(p+1) = p*\Gamma(p) \Gamma(1/2) = \sqrt{\pi} [/tex] 2.5!? Hmm. Let's see: [tex] 2.5! = \Gamma(2.5+1) = \Gamma(3.5) = \Gamma(7/2) = (5/2)\Gamma(5/2) = (5/2)(3/2)\Gamma(3/2) = (5/2)(3/2)(1/2)\Gamma(1/2) = (5/2)(3/2)(1/2)\sqrt{\pi} = (15/8)\sqrt{\pi} \approx 3.3233509704478425511840640312646. [/tex] Henri. Manned mission to Mars in 2019 Petition <-- Sign this, please.
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ID: 825010 · | |

HTH Volunteer tester Send message Joined: 8 Jul 00 Posts: 690 Credit: 845,606 RAC: 345 | |

Unfortunately, values other than integer + 0.5 doesn't work that way, or I don't see how... [tex] 0.6\Gamma(0.6) = \Gamma(0.6+1) = \Gamma(1.6) = from the table book = 0.89352. [/tex] [tex] \Gamma(0.6) = \Gamma(0.6+1)/0.6 = (1/0.6)\Gamma(1.6) = (1/0.6)*0.89352 = 1.4892. [/tex] [tex] \Gamma(-1/2) = \Gamma(-(1/2) + 1)/(-1/2) = -2\Gamma(1/2) = -2\sqrt{\pi}. [/tex] Henri. Manned mission to Mars in 2019 Petition <-- Sign this, please.
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ID: 825017 · | |

Sergej O. S. Volunteer tester Send message Joined: 29 Oct 08 Posts: 123 Credit: 44,886 RAC: 0 | |

Yes, Henri. | |

ID: 825042 · | |

Sergej O. S. Volunteer tester Send message Joined: 29 Oct 08 Posts: 123 Credit: 44,886 RAC: 0 | |

how to convert from positive ones? Oh, I did found that -z! = pi/sin(-z*pi)*(-z)/z! | |

ID: 825661 · | |

HTH Volunteer tester Send message Joined: 8 Jul 00 Posts: 690 Credit: 845,606 RAC: 345 | |

Hi! By the way, you don't know how to calculate nagative factorials? Or how to convert from positive ones? [tex] \Gamma(-1/2) = \Gamma(-(1/2) + 1)/(-1/2) = -2\Gamma(1/2) = -2\sqrt{\pi}. [/tex] [tex] \Gamma(-1.4) = \Gamma(-1.4+1)/-1.4 = -\Gamma(-0.4)/1.4 = -\Gamma(-0.4+1)/1.4(-0.4) = (1/(1.4*1.4))\Gamma(0.6) = 2.65929. [/tex] Hope This Help, Henri Tapani Heinonen. Manned mission to Mars in 2019 Petition <-- Sign this, please.
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ID: 826126 · | |

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Non-integer factorials?

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