Leibniz Formula

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Some Simple Remarks Contents 1 Leibniz Formula 1 2 Cauchy-Schwarz 2 3 Matrix exponentials 2 3.1 Hermite's recipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3.2 Newton's recipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.3 Putzer's recipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 4 Change of variables 4 5 Explicit Galois Theory 6 5.1 Statements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 5.2 Illustration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 6 The Galois group of Q over Q is homemorphic to the Cantor set 9 7 Parity 9 8 Simplicity 11 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . .

  • then u0

  • ?p nonnegative

  • let again

  • square matrix

  • nonnegative measurable function

  • function

  • newton's recipe


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Some Simple Remarks
Contents 1 Leibniz Formula 2 Cauchy-Schwarz 3 Matrix exponentials 3.1 Hermite’s recipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Newton’s recipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Putzer’s recipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Change of variables 5 Explicit Galois Theory 5.1 Statements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Illustration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 The Galois group of Q over Q is homemorphic to the Cantor set 7 Parity 8 Simplicity 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 First proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Second proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4 Third proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 A ring isomorphic to its square as a module 10Less´eriesdeFerrier 11 Continuity set
1 Leibniz Formula The n -th derivative of the product f 1 ∙ ∙ ∙ f k is the coefficient of X n in ) f k ( j n !  j = X n 0 fj 1( ! j ) X j ! ∙ ∙ ∙  j = X n 0 j ! X j ! . 1
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