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Schwarz reflection principle

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1: 1.10 Functions of a Complex Variable
Schwarz Reflection Principle
Phase (or Argument) Principle
§1.10(v) Maximum-Modulus Principle
Analytic Functions
Schwarz’s Lemma
2: 10.11 Analytic Continuation
3: 1.7 Inequalities
Cauchy–Schwarz Inequality
Cauchy–Schwarz Inequality
4: Bibliography F
  • C. K. Frederickson and P. L. Marston (1992) Transverse cusp diffraction catastrophes produced by the reflection of ultrasonic tone bursts from a curved surface in water. J. Acoust. Soc. Amer. 92 (5), pp. 2869–2877.
  • C. K. Frederickson and P. L. Marston (1994) Travel time surface of a transverse cusp caustic produced by reflection of acoustical transients from a curved metal surface. J. Acoust. Soc. Amer. 95 (2), pp. 650–660.
  • B. Friedman (1990) Principles and Techniques of Applied Mathematics. Dover, New York.
  • 5: 25.4 Reflection Formulas
    §25.4 Reflection Formulas
    25.4.1 ζ ( 1 s ) = 2 ( 2 π ) s cos ( 1 2 π s ) Γ ( s ) ζ ( s ) ,
    25.4.2 ζ ( s ) = 2 ( 2 π ) s 1 sin ( 1 2 π s ) Γ ( 1 s ) ζ ( 1 s ) .
    25.4.3 ξ ( s ) = ξ ( 1 s ) ,
    6: 26.6 Other Lattice Path Numbers
    7: Bibliography G
  • M. B. Green, J. H. Schwarz, and E. Witten (1988a) Superstring Theory: Introduction, Vol. 1. 2nd edition, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge.
  • M. B. Green, J. H. Schwarz, and E. Witten (1988b) Superstring Theory: Loop Amplitudes, Anomalies and Phenomenolgy, Vol. 2. 2nd edition, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge.
  • 8: 5.21 Methods of Computation
    For the left half-plane we can continue the backward recurrence or make use of the reflection formula (5.5.3). …
    9: Preface
    The term digital library has gained acceptance for this kind of information resource, and our choice of project title reflects our hope that the NIST DLMF will be a vehicle for revolutionizing the way applicable mathematics in general is practiced and delivered.
    10: 5.5 Functional Relations
    §5.5(ii) Reflection
    5.5.3 Γ ( z ) Γ ( 1 z ) = π / sin ( π z ) , z 0 , ± 1 , ,