Noninteger factorials? 

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Message boards : Science (nonSETI) : Noninteger factorials?
Author  Message 

Hi. I'm writing a program (as one of my hobbies) that calculates factorials. But people are telling me that noninteger factorials have no use  the Gamma function instead  G(z)=(z1)!.  
ID: 824881 ·  
My intuition tells me that rational, noninteger factorials would be useful in determining series convergencesalbeit with some fiddling with scale factors.  
ID: 824914 ·  
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 noninteger factorials never have been defined.  
ID: 824961 ·  
My intuition tells me that rational, noninteger factorials would be useful in determining series convergencesalbeit with some fiddling with scale factors. Thank you. I'll try to find the formula for practical use on that field...  
ID: 824977 ·  
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 noninteger 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 ·  
Hi. I'm writing a program (as one of my hobbies) that calculates factorials. But people are telling me that noninteger factorials have no use  the Gamma function instead  G(z)=(z1)!. 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^{p1}\,\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.  
ID: 825010 ·  
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.  
ID: 825017 ·  
Yes, Henri.  
ID: 825042 ·  
how to convert from positive ones? Oh, I did found that z! = pi/sin(z*pi)*(z)/z!  
ID: 825661 ·  
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.  
ID: 826126 ·  
Message boards : Science (nonSETI) : Noninteger factorials?
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