Does \(\frac{\sin(z)}{z}\) Have a Primitive in \(\mathbb{C} \setminus \{0\}\)?

[noamriemer]

Hello! I am having trouble understanding the whole primitive function thing in complex analysis.

How do I check if a certain function, say \frac {sin(z)} {z} [/tex] <br /> has a primitive, say in C/{0} ? <br /> What is the intuition? My intuition is that 0 is the only singularity, so if it is out of the picture, everything should be alright? (I saw that there is no primitive for it- but don&#039;t understand how to determine...) <br /> How do I prove there is a primitive? After all, I can&#039;t calculate infinite number of integrals over closed laps... Thank you!

 

[fresh_42]

I consider it as a technical tool to approach Lebesgue integration.
https://www.physicsforums.com/insights/omissions-mathematics-education-gauge-integration/https://en.wikipedia.org/wiki/Simple_function#Relation_to_Lebesgue_integration