I was wondering, how would one compute the value of

[dimension10]

I was wondering, how would one compute the value of $$\mbox{Si}(\infty+i\infty)$$ which is the same as $$\int\limits_{0}^{\infty+i\infty}\frac{\sin t}{t} \mbox{d}t$$ where i is the imaginary unit, the principal square root of minus one.

Thanks in advance.

 

[D H]

Wolfram alpha says the answer is complex infinity, "an infinite number in the complex plane whose complex argument is unknown or undefined."

The problem is that the sin integral does not behave very nicely for large imaginary numbers. It blows up. It is only well-behaved for large z if the imaginary part remains bounded.