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reflection properties

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11: 4.23 Inverse Trigonometric Functions
4.23.6 Arccot z = Arctan ( 1 / z ) .
§4.23(iii) Reflection Formulas
§4.23(v) Fundamental Property
12: 10.47 Definitions and Basic Properties
§10.47 Definitions and Basic Properties
Many properties of 𝗃 n ( z ) , 𝗒 n ( z ) , 𝗁 n ( 1 ) ( z ) , 𝗁 n ( 2 ) ( z ) , 𝗂 n ( 1 ) ( z ) , 𝗂 n ( 2 ) ( z ) , and 𝗄 n ( z ) follow straightforwardly from the above definitions and results given in preceding sections of this chapter. … …
§10.47(v) Reflection Formulas
13: Bibliography F
  • A. S. Fokas and Y. C. Yortsos (1981) The transformation properties of the sixth Painlevé equation and one-parameter families of solutions. Lett. Nuovo Cimento (2) 30 (17), pp. 539–544.
  • 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.