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1: 1.10 Functions of a Complex Variable
Phase (or Argument) Principle
§1.10(v) Maximum-Modulus Principle
Analytic Functions
Harmonic Functions
Schwarz’s Lemma
2: 3.8 Nonlinear Equations
Initial approximations to the zeros can often be found from asymptotic or other approximations to f ( z ) , or by application of the phase principle or Rouché’s theorem; see §1.10(iv). …
3: Bibliography R
  • W. Rudin (1976) Principles of Mathematical Analysis. 3rd edition, McGraw-Hill Book Co., New York.
  • 4: 27.10 Periodic Number-Theoretic Functions
    27.10.4 c k ( n ) = m = 1 k χ 1 ( m ) e 2 π i m n / k ,
    27.10.7 s k ( n ) = m = 1 k a k ( m ) e 2 π i m n / k ,
    27.10.9 G ( n , χ ) = m = 1 k χ ( m ) e 2 π i m n / k .
    5: 10.74 Methods of Computation
    To ensure that no zeros are overlooked, standard tools are the phase principle and Rouché’s theorem; see §1.10(iv). …
    6: 26.6 Other Lattice Path Numbers
    7: 10.11 Analytic Continuation
    8: Bibliography L
  • H. A. Lorentz, A. Einstein, H. Minkowski, and H. Weyl (1923) The Principle of Relativity: A Collection of Original Memoirs on the Special and General Theory of Relativity. Methuen and Co., Ltd., London.
  • 9: 3.6 Linear Difference Equations
    Similar principles apply to equation (3.6.1) when a n c n 0 , n , and d n 0 for some, or all, values of n . …
    10: Bibliography B
  • M. Born and E. Wolf (1999) Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light. 7th edition, Cambridge University Press, Cambridge.