Complex function ?

1. Mar 22, 2008

mkbh_10

1. The problem statement, all variables and given/known data

Locate & name the singularity of the function sin(sqrtZ)/Sqrt(Z) ?

2. Relevant equations

3. The attempt at a solution

At z= 0 i gives 0/0 form so should i apply L hospital's rule & then proceed ?

2. Mar 22, 2008

Hootenanny

Staff Emeritus
The is no need to consider the fraction as an entire entity, instead, one can separately calculate the order of the numerator and denominator independently and then combine them to find the order of the quotient.

Hence, start by determining the order of the numerator and denominator separately.

3. Mar 22, 2008

mkbh_10

determining the order of the numerator and denominator ?

4. Mar 22, 2008

Hootenanny

Staff Emeritus
One can determine the order of a function, at a point, by finding the order of the derivative which is non-vanishing at that point. For example, the function,

$$f(x) = x^2$$

Has order 2 at x=0 since,

$$f(0)=0 \;\;,\;\;f^\prime(0) = 0 \;\;,\;\;f^{\prime\prime}(0)=2\neq0$$

Do you follow?

Last edited: Mar 22, 2008
5. Mar 22, 2008

mkbh_10

The above function has Order =1 at z= 0 , then ?

6. Mar 22, 2008

Hootenanny

Staff Emeritus
Correct. So, if a function has a singularity of order one what type of singularity is it?

7. Mar 22, 2008

mkbh_10

i dn't know

8. Mar 22, 2008

Hootenanny

Staff Emeritus
A function with a positive order, at a given point, means that the Laurent series of the function at that point has no principle part, which means the singularity is ________.