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Differential Equations Lecture Work Solutions 58

Differential Equations Lecture Work Solutions 58 - r(r R R...

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Θ + µ Θ = 0 r ( r R ) µ R = 0 Θ (0) = 0 | R (0) | < Θ ( α ) = 0 R n = r ( n 1 2 ) π α only positive exponent Θ n = sin ( n 1 / 2) π α θ because of boundedness µ n = ( n 1 / 2) π α 2 n = 1 , 2 , . . . u ( r, θ ) = n =1 a n r ( n 1 / 2) π/α sin n 1 / 2 α π θ f ( θ ) = n =1 a n a ( n 1 / 2) π/α
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