Help, Im trying to win a contest, the answer to this will be appreciated!

Heres the question:

3.) The ___ function is defined as
[aforementioned function] = M(e^(-t); s) = integral [0, inf) e^(-t) t^(s-1) dt [50M points + GoldenPoliwag M 4]

#Notes: The asterisk * is used to indicate multiplication of real numbers. The text array "--" is used to represent an arrow; literally, "(A) to (B)."

Heres a visual: http://puu.sh/4niVD.png

Question

Help, Im trying to win a contest, the answer to this will be appreciated!

Heres the question:

3.) The ___ function is defined as
[aforementioned function] = M(e^(-t); s) = integral [0, inf) e^(-t) t^(s-1) dt [50M points + GoldenPoliwag M 4]


#Notes: The asterisk * is used to indicate multiplication of real numbers. The text array "-->" is used to represent an arrow; literally, "(A) to (B)."

Heres a visual: http://puu.sh/4niVD.png