What is the Significance of n+1/2 in the Generalized Binomial Formula?

[toni]

I stuck at the second "="...i know it goes like this because the formula...i just someone explain to me why it works like that.

thank you soooo much!

 

[HallsofIvy]

What is the definition of
$$\left(\begin{array}{c} x \\ n \end{array}\right)$$
when x is not an integer?

If you cannot answer that, can you say what
$$\left(\begin{array}{c} m \\ n \end{array}\right)$$
means when m and n are integers? What do you get if you replace the "m" with "x"?

 

[toni]

this is what I've done...still far from the destination

Sum(0 to infinity) (-1)^n [(1)(3)...(2n-1) x^(n+1/2) / (2n)!]

donno how to transform x^(n+1/2) to x^(n)?...thank you for your help!

 

[gabbagabbahey]

where did the n+1/2 come from?