I am studying Bessel Function in my antenna theory book, it said: I understand: Can you show me how do I get to I tried but it is not easy. Please help.
Last edited by Alan0354; July 19th 2013 at 04:52 PM.
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Originally Posted by Alan0354 I am studying Bessel Function in my antenna theory book, it said: I understand: Can you show me how do I get to I tried but it is not easy. Please help. You start with: Now change the variable to , then as before use: and use the symmetry properties ( and periodicity? )of the functions involved ... .
Originally Posted by zzephod You start with: Now change the variable to , then as before use: and use the symmetry properties ( and periodicity? )of the functions involved ... . Thanks for you time. Is it supposed to be I tried something similar but with no luck, can you show more steps? Thanks
Last edited by Alan0354; July 20th 2013 at 01:58 AM.
Originally Posted by Alan0354 Thanks for you time. Is it supposed to be I tried something similar but with no luck, can you show more steps? Thanks No I am just using the identity (note the wrong sign in the erlier post) to convert the sine to a cosine. Then the change of variable will be .
Originally Posted by zzephod No I am just using the identity (note the wrong sign in the erlier post) to convert the sine to a cosine. Then the change of variable will be So what is the next step? Thanks
is real. But I still don't get the part of it and the interval of [0, ].
Originally Posted by Alan0354 One mistake that seems to be following you...there is no in this equation. The function is defined as -Dan
Originally Posted by topsquark One mistake that seems to be following you...there is no in this equation. The function is defined as -Dan Sorry, it's a typo. But you know what I meant.
I worked on a few more steps: With this, for m=even. That is not going to get the answer. Also, how do you change to ?
Originally Posted by Alan0354 I worked on a few more steps: With this, for m=even. That is not going to get the answer. Also, how do you change to ? I was wrong in the last step, it should be how do I get to
Hi Zzephod , You are right. I since work on a few more steps As for For m=odd, and For m=even, For m=0 m=2 m=4 .......Therefore not What did I do wrong this time?
Last edited by Alan0354; July 21st 2013 at 01:56 PM.
Stupidity strikes again!!! I just realize !!!! So
Last edited by Alan0354; July 22nd 2013 at 01:38 AM.
Originally Posted by Alan0354 .....Therefore not What did I do wrong this time? Nothing, is symmetric so . Or more explicitly for even
How do I proof AND Thanks
Last edited by Alan0354; July 22nd 2013 at 12:20 PM.
There is no easy answer or easy way to integrate AND I tried Where you need to solve I tried Where you need to solve . Please help Thanks
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