Before you answer this OP, please read all the terms and conditions below. Thank you...
Today I hold an unofficial little contest on brilliant.org. Now, I will hold it here on Math S.E. It's just for fun guys. (>‿◠)✌
Before we start the contest, here are the rules of my little contest that you should obey as a contestant (the one who post an answer to this OP during contest period):
- The contest will be started on Sunday, October $26$, $2014$ at $12.00$ p.m. noon (UTC). So, until D-Day, please do not make any attempts (posting comments or answers) that can lead users here to answer the problem contest.
- You may post your answer after this OP is marked as a bounty question by me. I will give a bounty to this OP at least $250$ reps. The bounty will be awarded to the winner.
- The winner of this contest is the highest voted answer. So, the jury of this contest is not only me, but all of us.
- Each contestant can only post one answer and the answer can be posted anytime during the contest period. Once the answer is posted, it cannot be edited during the contest period. Since you have at least $4$ days to prepare the answer to this OP, please make sure you create a zero error answer.
- Do not post this contest problem on other sites for asking a hint or an answer.
- The contest will be ended on Sunday, November $2$, $2014$ (after bounty period over).
- The contestant will be disqualified for violating the contest rules above. The term disqualified means the contestant who violates the rules but she/ he owns the highest voted answer at the end of the contest will not be declared as the winner. Therefore, the bounty will not be awarded to her/ him.
If necessary, the rules may be changed accordingly. To be fair, I will not answer this OP nor give any hints to anyone. I really need your cooperation in order to make this contest succeed. Thank you.
Here is the contest problem:
Feel free to use any methods to solve this problem (real or complex analysis approach). Okay, happy problem solving and best of luck! ٩(˘◡˘)۶