Friday, September 28, 2007

In which I show you the results of hours of procrastination.

Both the Angry Baker and I have birthdays next week. Our (common) age in years will be given by

13 comments:

Not Important said...

AP,

Happy Birthday to you!
Happy Birthday to you!
Happy Birthday [your name here]!
Happy Birthday to you!

(I stole this rendition from Home Improvement.)

Anonymous said...

20.

Oops, both of us, 40.

Anonymous said...

Oops again ... common, yeah, 20.

Chaser said...

Clearly it's 29. Happy Birthdays.

Anonymous said...

Chaser,

Not quite! You don't need to solve the second equation for \lambda as it clearly must be an even square. Then you should be able to evaluate both the sum and the integral in your head, or on paper if need be.

YAMP.

Aidan said...

Now I'm no mathematician, but I play one on TV, and, assuming Gamma is the standard Euler gamma function, I think there's a mistake. Solving the 2nd equation gives a non-integer solution for l. But then in the 1st eqn we have to raise (x + anything) to the l power, over a domain of x ranging to negative infinity. That means we're taking a non-integer power of a negative number and the result includes imaginary numbers.

I know there can be circumstances in which the imaginary parts can cancel out, but this one doesn't look promising. If I'm wrong about that, this one is over my head.

Angry Professor said...

YAMP is correct. Lambda is an (integer) even square.

Anonymous said...

Apparently you have many angry years ahead, being only 44 you young whippersnapper, you! Happy Birthday and a nod in the general direction of Stephen Wolfram!

Angry Professor said...

Someone gets a cookie.

Franklin said...

It looks like somebody picked up my calculator and shook it until the insides went all kaflooey.

Many happy returns, smart lady and smart lady's husband.

Anonymous said...

Happy Birthday, math makes my head hurt.

Unknown said...

happy ninth birthday!

λ = 1.8163557+ also satisfies the bottom equation :)

flip phillips said...

anyone who can Zeta-function-ize their birthday is alright with me.