Raabe theorem
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21—30 of 121 matching pages
21: 27.11 Asymptotic Formulas: Partial Sums
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►where , .
►Letting in (27.11.9) or in (27.11.11) we see that there are infinitely many primes if are coprime; this is Dirichlet’s theorem
on primes in arithmetic progressions.
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27.11.15
►Each of (27.11.13)–(27.11.15) is equivalent to the prime number theorem (27.2.3).
The prime number theorem for
arithmetic progressions—an extension of (27.2.3) and first proved in de la Vallée Poussin (1896a, b)—states that if , then the number of primes with is asymptotic to as .
22: 27.12 Asymptotic Formulas: Primes
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Prime Number Theorem
…23: 1.10 Functions of a Complex Variable
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Picard’s Theorem
… ►§1.10(iv) Residue Theorem
… ►Rouché’s Theorem
… ►Lagrange Inversion Theorem
… ►Extended Inversion Theorem
…24: 1.4 Calculus of One Variable
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Mean Value Theorem
… ►Fundamental Theorem of Calculus
… ►First Mean Value Theorem
… ►Second Mean Value Theorem
… ►§1.4(vi) Taylor’s Theorem for Real Variables
…25: 35.2 Laplace Transform
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Convolution Theorem
…26: 24.10 Arithmetic Properties
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§24.10(i) Von Staudt–Clausen Theorem
…27: 1.6 Vectors and Vector-Valued Functions
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Green’s Theorem
… ►Stokes’s Theorem
… ►Gauss’s (or Divergence) Theorem
… ►Green’s Theorem (for Volume)
…28: 14.18 Sums
29: 23.20 Mathematical Applications
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