Math HELP!

[Impossible]

I got lost around the "k" part. I'm usually pretty good at Math, but these sorts of things always stump me.

[Non-Sequitur]

I got lost around the "k" part. I'm usually pretty good at Math, but these sorts of things always stump me.

A property of integers is that they can all be expressed as a multiple of another integer, m, plus an element, k, from the set of remainders when an integer is divided by m. mn + k

For example, all integers can be expressed as 7n + k where n is an integer and k is a remainder of an integer divided by 7. This set of remainders is {0, 1, 2, 3, 4, 5, 6 }.

[DSOK]

If you thought my explanation of that was confusing, you should see the problems that trouble me.

For example, I'm currently having a great deal of trouble with this situation. I have a real-valued function I want to integrate. The function is analytic in the lower half plane, except when it's real part vanishes, when it has a cusp. I'm integrating along the entire real axis, and the function's limiting behavior allows me to close the contour in the lower half plane at infinity. What terms do I pick up from the cusp, or, alternatively, can I split the contour into two quarter-circle contours, which would then each enclose an analytic region?


If anybody's got any ideas (:roll:), I'm all ears.

[EmperorJeramyu]

So, were you valedictorian?

[Non-Sequitur]

Is there a way to post the function?

[EmperorJeramyu]

I asked my brother. He skipped his sophomore year in college.

Jeff says:
Well, I'm not sure what the post means by "analytic region" or "lower half-plane" or "close the contour." If a function is real-valued over its entire doman, then it should be perfectly integratable, by hand if it is a known function, or numerically if it is not, or graphically estimated. However, if a function has a cusp in it, that means it its derivative is discontinuous at a point.

Jeff says:
But that shouldn't affect the integration.

Jeramyu *Go see Hero.* says:
This person has a doctorate in mathematics.

Jeff says:
That would probably explain why I really have no idea what he's talking about.

[DSOK]

So, were you valedictorian?

Alas, I was unable to give my high school's valedictory address, due to illness.

[diapadion]

Sickness? I don't remember that.

[Porter]

here we go....

[DSOK]

Sickness? I don't remember that.

I appreciate you giving me openings to keep my daily post count up, but is this really the forum for discussing this? I rather doubt that the other readers will care about the intricate details of who did what at my high school graduation.

[Non-Sequitur]

I would still like to know if there is any way you could show me the function you are trying to integrate. If you are having difficulty with it, I probably won't be able to figure it out, but my professors might be able to help.

[DSOK]

I would still like to know if there is any way you could show me the function you are trying to integrate. If you are having difficulty with it, I probably won't be able to figure it out, but my professors might be able to help.

Since you insist, I will post the original integral that I wanted to evaluate. I wouldn't waste your time trying to work it out though. I am a professional mathematical physicist, and I have a good idea when an expression is intractable. But if you know any professors who specialize the Fourier analysis of functions with essential singularities, then, by all means, ask their opinion.

The expression will follow shortly.

[Glenn47]

Oooh...a professional mathematical physicist. How important...

[DSOK]

[Non-Sequitur]

Thank you. I will have several of my professors look at it.