A Special Hills Equation With Discontinuous Coefficients
A Special Hills Equation With Discontinuous Coefficients
Harry Hochstadt
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) y'(0) = y(L) = ^. ) y(o) = y'(L) = 0. The corresponding characteristic equations are 1. ) tan X = a tanh Xa(L - l) 2. ) tan X = - i tanh Xa(L - l) a 5. ) tan X = a coth Xa(L - 1) h-. ) tan X = - - coth Xa(L - 1). 13. To evaluate the roots of these equations, we write, as before, in case 1. ) 1 1 Xa(L - l) = tanh — tan \ and graph the right side of the equation. We then obtain Flg:ure k, where all four cases are included. Figure h H^. 2 For a (L - l) . , 1 a direct analysis shows that ve have... two roots corresponding to case 1. ) in the interval [o, tan a] . Then the sequence becomes = x^"""^
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