| H(y) = |
(7.14) |
| H'(y) | = | ||
| H''(y) | = | (7.15) |
| How to deal with equations involving polynomials. If I ask you when is a + by + cy2 = 0 for all y, I hope you will answer when a = b = c = 0. In other words a polynomial is zero when all its coefficients are zero. In the same vein two polynomials are equal when all their coefficients are equal. So what happens for infinite polynomials? They are zero when all coefficients are zero, and they are equal when all coefficients are equal. |
So lets deal with the equation, and collect terms of the same order in y.
|
(7.16) |
| 2 |
(7.17) |
|
Theorem: The behaviour of the coefficients
as of a Taylor series
u(y) = |
Now for large s,
| as + 2 = |
(7.18) |
| ey2 = |
(7.19) |
| bs + 2 = |
(7.20) |