Dr. Katz DEq Homework Solutions 87

Dr. Katz DEq Homework Solutions 87 - Algebraic Solutions of...

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Algebraic Solutions of Differential Equations 87 6.4. Solutions of the Hypergeometric Equation in Characteristic p (6.4.0) Proposition (compare [23]). Let a, b, c be integers contained in {0, 1, . .., p- 1}. In order that the hypergeometric equation with parameters -a,-b,-c admit two "mod p" solutions in Fp[2] which are linearly independent over Fp(2), it is necessary and sufficient that either b> c > a or a>c>b. Proof Let d--f(-a, -b, -c) denote the hypergeometric differential operator with parameters - a, - b, - c; r=((-a,-b,-c)=2(1-,~) ( + [-c-(1-a-b) 2] J-~-ab. is an Fp [2P]-linear endomorphism of Fp [2], which maps the Fp-module N of polynomials of degree at most p- 1 to itself (in an Fp-linear manner).
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This note was uploaded on 12/21/2011 for the course MAP 4341 taught by Professor Normankatz during the Fall '11 term at UNF.

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