An Extension of the Strum Liouville Expansion
An Extension of the Strum Liouville Expansion
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In our eReader you can find the full English version of the book. Read An Extension of the Strum Liouville Expansion Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book An Extension of the Strum Liouville Expansion
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Without loss of generality we may assume tfi(w2x*>2x) 9*0, X «* X*. (31) Now define a solution of (1) by u{x) = Ui(x) + — 1*2(3;), C2 (32) «(&) = Di(3;) + - i; 2 (3;), C 2 and choose £1 _ UijuiVi) _ c 2 Ui(u 2 v 2 ) Camp: An Externum ef the 8twrm~LioumUe Expansion. 35 For values of X sufficiently near X*, Ui(u 2 v 2 ) ¥" 0, otherwise (31) would be violated by Hoik's Theorem. Hence for all X in the interval considered Ui{U 2 V 2 ) Consequently for all such X, Ui(u x r x ) m 0. Again U 2 (uv) = U...ttonvd - -^^ U 2 {u 2 v 2 ) = ^22%, X * X*.
At X = Xt, And Ui(u 2 v 2 ) lUi(ihv 2 )j For X = X t, U 2 (u x v x ) = - D ', (K) t g (X)^i(«txx^xx) + g / (X)^i(tt, x), Ul(lli\V2\) 2Ul(u 2 V 2 )U l (tl 2>i V 2>i ) Tliis vanishes if Z)"(X) = at X = X*. Applying the argument a third time we obtain y 1 (w 2 -K» 2 )^ = o, which is absurd since by (32) u(0) = 1.
i . \ Z)"(X) ^ at X = X*.
Since for Case III when X = X* every solution of (1) satisfies (2), if we define a solution of (15) by \u{x) m y ( x ) + &i«i(a-) -f b 2 u 2 (x), , QQ .
What to read after An Extension of the Strum Liouville Expansion?
You can find similar books in the "Read Also" column, or choose other free books by Chester Claremont Camp to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Without loss of generality we may assume tfi(w2x*>2x) 9*0, X «* X*. (31) Now define a solution of (1) by u{x) = Ui(x) + — 1*2(3;), C2 (32) «(&) = Di(3;) + - i; 2 (3;), C 2 and choose £1 _ UijuiVi) _ c 2 Ui(u 2 v 2 ) Camp: An Externum ef the 8twrm~LioumUe Expansion. 35 For values of X sufficiently near X*, Ui(u 2 v 2 ) ¥" 0, otherwise (31) would be violated by Hoik's Theorem. Hence for all X in the interval considered Ui{U 2 V 2 ) Consequently for all such X, Ui(u x r x ) m 0. Again U 2 (uv) = U...ttonvd - -^^ U 2 {u 2 v 2 ) = ^22%, X * X*.
At X = Xt, And Ui(u 2 v 2 ) lUi(ihv 2 )j For X = X t, U 2 (u x v x ) = - D ', (K) t g (X)^i(«txx^xx) + g / (X)^i(tt, x), Ul(lli\V2\) 2Ul(u 2 V 2 )U l (tl 2>i V 2>i ) Tliis vanishes if Z)"(X) = at X = X*. Applying the argument a third time we obtain y 1 (w 2 -K» 2 )^ = o, which is absurd since by (32) u(0) = 1.
i . \ Z)"(X) ^ at X = X*.
Since for Case III when X = X* every solution of (1) satisfies (2), if we define a solution of (15) by \u{x) m y ( x ) + &i«i(a-) -f b 2 u 2 (x), , QQ .
What to read after An Extension of the Strum Liouville Expansion?
You can find similar books in the "Read Also" column, or choose other free books by Chester Claremont Camp to read onlineMoreLess
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