Major math error with Grapher

[Papajohn56]

Using a factorial in Grapher results in an incorrect function output, it seems Grapher does the Gamma function rather than the standard step function for factorial. Take a look:

Which gamma is actually defined as:

rather than the true factorial:

 

[gauchogolfer]

How would you plot a factorial for negative numbers, anyways? Isn't that the whole point of the Gamma function, to account for real and complex numbers? Still, I'm not sure it counts as a 'Major Math Error'. Is there a different function indicator rather than ! that you could use for factorial?

 

[Papajohn56]

How would you plot a factorial for negative numbers, anyways? Isn't that the whole point of the Gamma function, to account for real and complex numbers?

Exactly, that's the biggest problem, along with positive decimal factorials.

 

[corneng]

http://en.wikipedia.org/wiki/Factorial


scroll down to gamma function part

 

[gauchogolfer]

http://en.wikipedia.org/wiki/Factorial


scroll down to gamma function part

Thanks for the link, but I think we both know what the Gamma function is already. The OP would like to know why ! defaults to Gamma and not factorial, I imagine. Maybe it's because factorial is only defined for positive integers, and Grapher can only handle continuous functions? Iono.

 

[Papajohn56]

Thanks for the link, but I think we both know what the Gamma function is already. The OP would like to know why ! defaults to Gamma and not factorial, I imagine. Maybe it's because factorial is only defined for positive integers, and Grapher can only handle continuous functions? Iono.

yeah, I know factorial and gamma are related, but they aren't the same. That's my concern

 

[MisterMe]

... The OP would like to know why ! defaults to Gamma and not factorial, I imagine. Maybe it's because factorial is only defined for positive integers, and Grapher can only handle continuous functions? ...

The gamma function is defined over the range of negative non-integers, zero, and positive numbers. The factorial is not a step function. In the OP's parlance, the factorial function is defined only for zero and positive integral arguments. The OP cannot invoke non-integral arguments and then complain about the result.

 

[Papajohn56]

The gamma function is defined over the range of negative non-integers, zero, and positive numbers. The factorial is not a step function. In the OP's parlance, the factorial function is defined only for zero and positive integral arguments. The OP cannot invoke non-integral arguments and then complain about the result.

Yes but Gamma and Factorial are not the same thing. As a matter of fact, for positive integers, Gamma is equal to (n-1)!, rather than just n!

They are not the same function, even though they are related. When I enter factorial, I shouldn't get Gamma as the output.