Notation: Can i write Si(inf) as an alternative to the integral from 0 to inf of sinx

[Mr_Random_Guy]

Can i write Si(inf) as an alternative to the integral from 0 to inf of sinx/x dx? Or would i have to write the limit as z --> inf of the integral from 0 to z of sinx/x dx?

 

[Steven G]

Can i write Si(inf) as an alternative to the integral from 0 to inf of sinx/x dx? Or would i have to write the limit as z --> inf of the integral from 0 to z of sinx/x dx?

integral from 0 to inf of (sinx/x) dx is best, while limit as z --> inf of the integral from 0 to z of (sinx/x) dx is equivalent. Not sure what Si(inf) means.

 

[Dr.Peterson]

Can i write Si(inf) as an alternative to the integral from 0 to inf of sinx/x dx? Or would i have to write the limit as z --> inf of the integral from 0 to z of sinx/x dx?

You're referring to the sine integral function Si, as in http://mathworld.wolfram.com/SineIntegral.html , right?

It's not proper (that's almost a pun) to use infinity as an argument of a function. So you should state the limit; but as you'll see on that page, you could also say -si(0), or just pi/2.

 

[Mr_Random_Guy]

You're referring to the sine integral function Si, as in http://mathworld.wolfram.com/SineIntegral.html , right?

It's not proper (that's almost a pun) to use infinity as an argument of a function. So you should state the limit; but as you'll see on that page, you could also say -si(0), or just pi/2.

Ahh I didn't see the (lower case s) si(z) part, thank you.