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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: 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 ) ,
5: 26.6 Other Lattice Path Numbers
6: 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.
  • 7: 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). …
    8: 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.
    9: 5.5 Functional Relations
    §5.5(ii) Reflection
    5.5.3 Γ ( z ) Γ ( 1 - z ) = π / sin ( π z ) , z 0 , ± 1 , ,
    10: 28.12 Definitions and Basic Properties
    28.12.2 λ ν ( - q ) = λ ν ( q ) = λ - ν ( q ) .
    28.12.10 me ν ( z , q ) ¯ = me ν ¯ ( - z ¯ , q ¯ ) .
    28.12.15 se ν ( z , q ) = - se ν ( - z , q ) = - se - ν ( z , q ) .