The Natural Charge Distribution And Capacitance of a Finite Conical Shell
The Natural Charge Distribution And Capacitance of a Finite Conical Shell
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3).
If now, ^ ((j, )^^^"^, q > -1/2, as \^\ — ■>oo in the right half plane, then, since K (u. , 9 )'VM. ~'^ . We can assert that the left hand side of (6. 3) vanishes at infinity. ^Tinally if we ass'-jne G (m, ) 'v- m, ""^ as \^\ — •>oo in the left half plane, with p > 1/2, then since K~(|j, Q )«v, (-m-)" as \^\ — ■>oo, we see that the right hand side vanishes at Infinity. Invoking Liouville's theorem we have that the entire function defined by either side of equation (6. 3) is Identically zero.... Hence {6, h) 5^(^) = 8 ine^z" (-|; 9„ )k'' (n, « ) (m. 4) 2 z -1/2 Since K* (n, 9^ ) ~ ^""^^ ^ in the region Re^t > then, cle&rly, ^ ^iii)>^ ^x"^'^ in this region. Also note that G (\i) is given explicitly by u. K~(m. , 9 ) G i^) K-(-|.
- 1 (continued on next page) (6. 5) A(u) - 26 - Note, since (K (m, 6 ))~ is zeroless for Rep> - -r, that ^ (m. ) is analytic for 1 ° T" - - . SulDstituting 2. _^(m. ) into (3. 20) page 1^ (setting p. = w - l/2) and solving for A(u) we get 2TTUO .
What to read after The Natural Charge Distribution And Capacitance of a Finite Conical Shell?
You can find similar books in the "Read Also" column, or choose other free books by Samuel Karp to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
3).
If now, ^ ((j, )^^^"^, q > -1/2, as \^\ — ■>oo in the right half plane, then, since K (u. , 9 )'VM. ~'^ . We can assert that the left hand side of (6. 3) vanishes at infinity. ^Tinally if we ass'-jne G (m, ) 'v- m, ""^ as \^\ — •>oo in the left half plane, with p > 1/2, then since K~(|j, Q )«v, (-m-)" as \^\ — ■>oo, we see that the right hand side vanishes at Infinity. Invoking Liouville's theorem we have that the entire function defined by either side of equation (6. 3) is Identically zero.... Hence {6, h) 5^(^) = 8 ine^z" (-|; 9„ )k'' (n, « ) (m. 4) 2 z -1/2 Since K* (n, 9^ ) ~ ^""^^ ^ in the region Re^t > then, cle&rly, ^ ^iii)>^ ^x"^'^ in this region. Also note that G (\i) is given explicitly by u. K~(m. , 9 ) G i^) K-(-|.
- 1 (continued on next page) (6. 5) A(u) - 26 - Note, since (K (m, 6 ))~ is zeroless for Rep> - -r, that ^ (m. ) is analytic for 1 ° T" - - . SulDstituting 2. _^(m. ) into (3. 20) page 1^ (setting p. = w - l/2) and solving for A(u) we get 2TTUO .
What to read after The Natural Charge Distribution And Capacitance of a Finite Conical Shell?
You can find similar books in the "Read Also" column, or choose other free books by Samuel Karp to read onlineMoreLess
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