On the Functions of the Parabolic Cylinder
On the Functions of the Parabolic Cylinder
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In our eReader you can find the full English version of the book. Read On the Functions of the Parabolic Cylinder 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 On the Functions of the Parabolic Cylinder
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19) \^rK) t). V. I(Y>{) for V = - X- + i^-, X real and tending to +oo. For X -s> oo. , -1 nX fX. In ^. L/2. Ix(Y«)^-l/2-ix(M> ^ 2" exp^- | log X . ^ - ^r^rU *V (2. 20) i(^-X* (^)^/^(4 *^)) I • The corresponding expression for X ->-oo can be obtained by putting X » -t and letting t -> +oo, or by interchanging ^ and vi and letting \. ->oo as above. 3, Special one-valued solutions Before entering upon a discussion of the addition theorems it will be of some value to remark on the equation of one-v...aluedness. From the transformation (2, 3) we see that a point in the (x, y)-5ystem has two pairs of coordinates in the (^, y^ ) -system, namely (C>>1 ) and i-E, f-^)» Thus, to say that the function F(4, >y ) is one-valued in the (x, y)-plane means that F(^, >7) » F(-C, -v]). Therefore, a product fj^(YC)f2(Y">7) is a one-valued function in the (x, y)-plane if and only if the functions f and fp are both even or both odd. Given f, (Y?) and f2(Y^)» then clearly - 9 - (3. 1) f^(Y4)f2(Y^) + f^i-r^)f^i'ryi) is a one-valued solution of the wave equation, although one in which the variables are not completely separated.
What to read after On the Functions of the Parabolic Cylinder?
You can find similar books in the "Read Also" column, or choose other free books by David I Epstein to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
19) \^rK) t). V. I(Y>{) for V = - X- + i^-, X real and tending to +oo. For X -s> oo. , -1 nX fX. In ^. L/2. Ix(Y«)^-l/2-ix(M> ^ 2" exp^- | log X . ^ - ^r^rU *V (2. 20) i(^-X* (^)^/^(4 *^)) I • The corresponding expression for X ->-oo can be obtained by putting X » -t and letting t -> +oo, or by interchanging ^ and vi and letting \. ->oo as above. 3, Special one-valued solutions Before entering upon a discussion of the addition theorems it will be of some value to remark on the equation of one-v...aluedness. From the transformation (2, 3) we see that a point in the (x, y)-5ystem has two pairs of coordinates in the (^, y^ ) -system, namely (C>>1 ) and i-E, f-^)» Thus, to say that the function F(4, >y ) is one-valued in the (x, y)-plane means that F(^, >7) » F(-C, -v]). Therefore, a product fj^(YC)f2(Y">7) is a one-valued function in the (x, y)-plane if and only if the functions f and fp are both even or both odd. Given f, (Y?) and f2(Y^)» then clearly - 9 - (3. 1) f^(Y4)f2(Y^) + f^i-r^)f^i'ryi) is a one-valued solution of the wave equation, although one in which the variables are not completely separated.
What to read after On the Functions of the Parabolic Cylinder?
You can find similar books in the "Read Also" column, or choose other free books by David I Epstein to read onlineMoreLess
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