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

AI Thread Summary
The discussion centers on understanding the significance of n+1/2 in the Generalized Binomial Formula. Participants seek clarification on the definition of binomial coefficients when x is not an integer and how to interpret the expression involving m and n as integers. There is confusion regarding the transformation of x^(n+1/2) to x^n and the origin of the n+1/2 term in the formula. The conversation highlights the need for a deeper explanation of these mathematical concepts. Overall, the thread emphasizes the complexities involved in applying the Generalized Binomial Formula.
toni
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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!
 

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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"?
 
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!
 
where did the n+1/2 come from?
 

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