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Mellin vu du ciel Mellin, seen from the sky
Philippe Flajolet INRIA Rocquencourt
March 10, 2008
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Hjalmar MELLIN 1854--1933
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Mellin vu du ciel Mellin, seen from the sky Philippe Flajolet - - PowerPoint PPT Presentation
Mellin vu du ciel Mellin, seen from the sky Philippe Flajolet - - PowerPoint PPT Presentation
Mellin vu du ciel Mellin, seen from the sky Philippe Flajolet INRIA Rocquencourt March 10, 2008 1 Hjalmar MELLIN 1854--1933 2 I. INTRODUCTION 3 4 WHY? 5 6 . 7 II. BASICS 8 9 10 11 12 - - 13 III. HARMONIC SUMS Asymptotics 14
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- I. INTRODUCTION
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WHY?
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.
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- II. BASICS
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- -
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- III. HARMONIC SUMS
Asymptotics
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<0,+oo> <1,+oo>
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<-1,0>
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<-2,-1>
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Digital trees (tries)
- Set up recurrence and generating function
- Solve and get a sum
- Approximate (equiv. Poisson approx.)
- Analyse harmonic sum
Digital trees aka “tries”
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- IV. SOME GOODIES
A near(?) identity Möbius
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A (near) identity ???
- Cf. Brigitte Vallée: binary Euclidean GCD
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A (near) identity ???
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1, -1, -1, 0, -1, 1, -1, 0, 0, 1, -1, 0, -1, . . .
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eorem: The sum tends to INFINITY like
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dist=10^(-5)
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[Clement+Flajolet-Vallee, 2000-2001]
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- V. Advanced techniques
Perron’s formulae Approximating Dirichlet series Poisson + Mellin = Newton + Nörlund (Rice)
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- VI. More goodies
Magic Duality and the Golden T riangle
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