If you thought factorials of decimals and integers can be found out only by integral of e or integral of log functions, think again !!
Here is a formula which uses summation till infinity and still finds factorials of decimals and integers. How about that ?
This formula is very liked by me also because I did an experiment to derive it.
(I had done this formula earlier and have made a blog post. In this blog post I have reframed the expression in some other manner)
2 comments:
How can there be decimal factorials?
Just because humans do whole numbers and 3! as 3*2*1, it does not mean that nature does not operate on decimal numbers and 3.5!, for instance.
Where does decimal factorial come into picture in real world?
Taylor series gives a picture of the nature principles. e derived from Taylor series and log series works on decimal factorials too.
Why does the above formula give results for decimal factorial?
Quite frankly, I do not know. Wolfram Alpha gives answer for decimals when the above summation till infinity is used for decimals. And Stephen Wolfram, the man behind Wolfram is a very big guy in mathematics.
Which of your formula do I think can be used for decimal factorials calculations using just a normal calculator?
2n! = (((n+1)(n+2))/2)^10 , which is approximate and un-accurate , I believe should give us decimal factorials approximately which can be calculated using a normal calculator provided we make corrections to the formula.
The above mentioned formula can be used for 0 to 1. Fractions 1/n as decimals. And for positive integers.
This is an accurate formula in above ranges.
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