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which gives

S - P2) ^ + (S - 7p) ^ - (S - 7 + 4|i V = 0. (9.33)

Considering the function (p1 in the form of an odd expansion

we implicitly satisfy, as for Ço, a first boundary condition Çi |p=o — 0 of a null slope of the deformation at the origin, a condition which would not be achieved by a holed lens (in this latter case a ln p term must be included in the odd expansion). For n > 1 we obtain a recurrent relation between the coefficients, ain+i _ ß + (n + 3)(n- 1)

a2n-1

a + 5) ■■■[y + (n + 3)(n - 1)] a a2n+1 = -¡7-, 1s.gn-a1-

Setting a1 = 1, the basic solution of the equation without left side is

+ ß(ß + 5) • • • [ß + (n + 3)(n - 1)] ,n+i '+ n!(n + 1)! Sn P

The general solution of (9.30a) is a linear combination of (p0 and ^ which both already satisfy the boundary condition of null slope at the origin. Hence, it can be represented by

0 0

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