Dr. Katz DEq Homework Solutions 96

Dr. Katz DEq Homework Solutions 96 - 96 N.M. Katz:...

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96 N.M. Katz: (6.7.1.1) Yo J Let Co (a, b, c) (resp. C l (a, b, c)) be the matrix of "analytic contintiation along 7o (resp. Vl)" of the space of germs of solutions at in terms of the basis (6.7.1.0). Then (cf. [1], p. 93-94), 0 (6.7.1.3) Cl(a,b,c)=IB1 l(a,b,c) B2 l(a,b,c)~ \B,12(a,b,c) B2'2(a,b,c)] where the coefficients B~.j(a, b, c) are given by (6.7.1.4) B1 l(a, b, c)= 1-2iexp(~i(c-a-b)) sin(~za) sin(~b) ' sin (n c) ' sin(n(c-a)) sin (re(c- b)) (6.7.1.5) B2, z (a, b, c) = 1 + 2 i exp (~ i(c - a - b)) sin (~ c) ' (6.7.1.6) B1 2(a,b,c)=-2~iexp(~i(c-a-b)) r(c)r(c-1) ' r(c- a) r(c - b) r(b) r(a)' B2,1 (a, b, c) (6.7.1.7) r(2- c) r(1 - c) = 2n i exp(n i(c- a- b))
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