Gamma function

1. Aug 4, 2015

Muthumanimaran

This is given in Mathematical methods for physicists by Arfken and weber, while defining a property of gamma function, I have no idea how the term in the red circle becomes 'z' in the final step, please help

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2. Aug 4, 2015

gleem

Try multiplying the numerator and denominator by z and pull out an n from the exponent then rearrange terms.

3. Aug 4, 2015

Muthumanimaran

I'm asking about the final step, How to get the final step from the second step?

4. Aug 4, 2015

gleem

The limit of the product is product of the limit of the factors. What is the definition of the gamma function?

5. Aug 4, 2015

Muthumanimaran

I know the limit of the second term in the product converges to "gamma of z', it is how the gamma function is defined, But I couldn't figure out how the limit of the first term in the product converges to 'z'. How do I compute it?

6. Aug 4, 2015

HallsofIvy

$$\lim_{n\to \infty} \frac{nz}{z+ n+ 1}$$

Divide both numerator and denominator by n:
$$\lim_{n\to\infty}\frac{z}{\frac{z}{n}+ 1+ \frac{1}{n}}$$

7. Aug 4, 2015

gleem

nz/(n+z+1) → nz/n in the limit n→∞

8. Aug 5, 2015

Muthumanimaran

Yeah that's what I asked for, Thank you!