Factorial of Frational number!!!
Hello my dear friends as we know about FACTORIAL its a nice concept which is very usefull for solving many problems and we also have a generL or we can say basic idea about it.. n!=n(n-1)(n-2)......32*1 but have ypu ever wondered that this topic limits only to positive numbers or even we can get the value of negative numbers!!! Or fractional part also belongs to postive side so it should also have some methods to solve and get its value like (1/2)! Or (5/2)!.... Please tell ... How to get these !!!! Thanks all of you :-)
Note by
Yash Kumar Gupta
8 years, 3 months ago
No vote yet
3 votes
Easy Math Editor
This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.
When posting on Brilliant:
*italics*or_italics_**bold**or__bold__paragraph 1
paragraph 2
[example link](https://brilliant.org)> This is a quote# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"\(...\)or\[...\]to ensure proper formatting.2 \times 32^{34}a_{i-1}\frac{2}{3}\sqrt{2}\sum_{i=1}^3\sin \theta\boxed{123}Comments
See Gamma Functions.
negative is allowed, you want -1! thats (-1), you want -2! = (-1)(-2) = (+2), you want -5! , thats = -120, actually if you want (-N)! , its just = ((-1)^N)) * N! , nothing new. And fractionals are also allowed, but you better give me a step to work on, that is, in natural factorials the step = 1, and you go on multiplying 1,2,3,4... as they increment by 1. If you want a step of 0.1, then I will define (2.5)! = (1)(1.1)(1.2)....(2.4)(2.5); if you want an even smaller step, then (2.5)! = (1.01)(1.02).....(1.10)(1.11).....(2.47)(2.48)(2.49)(2.5)
Although the above one is the same result you would get by multiplying natural numbers from 101 to 250 and dividing by (100)^(-250), there is no funny trick here, its what a fractional stepwise factorial is for us computer folks. So you can define your rules, thats good for health, and we appreciate it too, but its nothing new actually, it just takes some skill to see that its the same thing. Or you can say (m/n)! = (m!)/(n!), or any other rule, thats all healthy, thats allowed.
Log in to reply
Actually I dont care much about the hard and fast rules of the mathematicians, I say "okay, you want it like that, fine, I will allow you to, but here is my condition - and thats it, If you dont want to define it like that, you dont like my definition, then thats your headache, I will define it my way.", So feel free to make up your own maths, because thats exactly what its for, :)