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Could someone explain how I would go about solving for x of x=(5/6)!

Thanks

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- Thread starter On Radioactive Waves
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- #1

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Could someone explain how I would go about solving for x of x=(5/6)!

Thanks

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- #3

jcsd

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Factorials only work for natural numbers, so 5/6 does not have a factorial.

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Njorl

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Njorl

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selfAdjoint

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It has the property that n! = Γ(n+1).

This isn't going to be a lot of help in solving the equation though.

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jcsd

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- #7

jcsd

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Actually just done some research, using the gamma function you can find values for half-integrals.

- #8

ahrkron

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Originally posted by selfAdjoint

The Gamma function is defined by Γ(z) = ∫_{0}^{oo}t^{z-1}dt

There is a small, yet important omission here. The definition includes a negative exponential:

Γ(z) = ∫

The exponential is important because it makes the integral converge for almost all values of z (the exponential goes to zero much faster than the growth of t

In particular, for what you want, you can obtain the value as

(5/6)! = Γ(5/6 + 1) = ∫

Mathworld has a nice entry for the Gamma function. In the plot, you can see that the value for Γ(1+5/6) = Γ(1.833) is slightly less than one.

- #9

selfAdjoint

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In the half plane of complex numbers with real part > 1, it can be defined by Γ(z-1) = π/(Γ(z)sin(πz)) = πz/(Γ(1+z)sin(πz)).

- #10

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I've looked at the mathworld site, many time actually.

It turns out this problem stems back a few years, and I just realised its not factorial I'm actually wondering about (tried it on my TI-89)

Okay, here is there real problem then. My calculator will give sums for negative numbers and fractions, and I was confused about that.

This is actually a lot less confusing than i thought. Thanks for the input everyone. I remembered wrong but hey its been a while.

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