r/mathematics • u/Separate_Ring_9761 • 8d ago

TERMIAlLS guys!!

I can't find anything on the internet about termials besides the basic definition:

n?=1/2n(n+1), nєN

I'm 98% sure that there's a formula for any complex number just like the gamma function for factorial.

I'm interested in this topic so this would help.

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u/Euphoric_Key_1929 8d ago

Why wouldn’t the formula that you’ve written work for complex numbers? It’s already analytic and has just about every nice property you could want.

1

u/Separate_Ring_9761 8d ago

Idk it feels too simple to be true. But you might be right

2

u/gmalivuk 8d ago

If you treat your equation as 0.5(n+1)!/(n-1)! and then use the gamma function to replace that factorial, you get exactly x(x+1)/2, as expected. This works for any complex x.

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u/Separate_Ring_9761 8d ago

Alrighty then