# 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!