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About the Cover: The Ruscheweyh Derivatives

To the Memory of Stephan Ruscheweyh

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Abstract

Honoring Stephan Ruscheweyh’s magnificent contributions to complex analysis in general and to geometric function theory in particular, the cover of this volume shows a (modified) phase plot of a Ruscheweyh derivative of the complex tangent function. In this note we sketch some background.

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Fig. 1
Fig. 2

Notes

  1. The name was proposed by Al Amiri [2].

References

  1. Ahuja, O.P.: On the generalized Ruscheweyh class of analytic functions of complex order. Bull. Aust. Math. Soc. 47, 247–257 (1993)

    Article  Google Scholar 

  2. Al-Amiri, H.S.: On Ruscheweyh derivatives. Ann. Polon. Math. 38, 87–94 (1980)

    Article  MathSciNet  Google Scholar 

  3. Kim, Y.C., Lee, K.S., Srivastava, H.M.: Some applications of fractional integral operators and Ruscheweyh derivatives. J. Math. Anal. Appl. 197, 505–517 (1996)

    Article  MathSciNet  Google Scholar 

  4. Ruscheweyh, St.: Convolutions in geometric function theory. Séminaire de Mathématiques Supérieures, 83 (1982) Fundamental Theories of Physics. Presses de l’Université de Montréal, Montréal

  5. Ruscheweyh, St, Sheil-Small, T.: Hadamard products and the proof of the Pólya-Schoenberg conjecture. Comment. Math. Helv. 48, 119–135 (1973)

    Article  MathSciNet  Google Scholar 

  6. Ruscheweyh, St: New criteria for univalent functions. Proc. Am. Math. Soc. 49, 109–115 (1975)

    Article  MathSciNet  Google Scholar 

  7. Wegert, E.: Phase diagrams of meromorphic functions. Comput. Methods Funct. Theory 10, 639–661 (2010)

    Article  MathSciNet  Google Scholar 

  8. Wegert, E.: Visual Complex Functions: An Introduction with Phase Portraits. Springer, Basel (2012)

    Book  Google Scholar 

  9. Wegert, E., Semmler, G.: Phase plots of complex functions: a journey in illustration. Not. AMS 58, 768–780 (2011)

    MathSciNet  MATH  Google Scholar 

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Correspondence to Elias Wegert.

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Communicated by Doron Lubinsky.

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Wegert, E. About the Cover: The Ruscheweyh Derivatives. Comput. Methods Funct. Theory 20, 1–4 (2020). https://doi.org/10.1007/s40315-019-00295-8

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  • DOI: https://doi.org/10.1007/s40315-019-00295-8

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