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Radius of \(\gamma \)-spirallikeness of order \(\alpha \) of some special functions

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Abstract

In light of the Alexander transformation, the class of spirallike functions is significant. The characteristics of special functions also appear very frequently in Geometric function theory. In this paper, we find the radii of \(\gamma \)-spirallike and convex \(\gamma \)-spirallike of order \(\alpha \) of certain special functions.

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Acknowledgements

We are thankful to the Editor and the Reviewers for their valuable suggestions to improve the previous version of this manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Literature, Kafkas University, Campus, 36100, Kars, Turkey

    Sercan Kazımoğlu

  2. Department of Mathematics, Bhagwan Parshuram Institute of Technology, Rohini-17, New Delhi, India

    Kamaljeet Gangania

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  1. Sercan Kazımoğlu
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  2. Kamaljeet Gangania
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Appendix

Appendix

In the following, we demonstrate some of the obtained results numerically and graphically. Tables 1 and 2 demonstrate Theorem 7 and Theorem 11, respectively (Fig. 1).

Table 1 Radii of \(\mathcal {P}_{2n-1}\) for \(\alpha =0\) in view of Theorem 7
Full size table
Table 2 Radii of \(U_{\delta }(z),~V_{\delta }(z)\), and \(W_{\delta }(z)\) for \(\delta =\frac{1}{2}\)
Full size table
Fig. 1
figure 1

Graphs explaining Theorem 7 and Theorem 11

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Kazımoğlu, S., Gangania, K. Radius of \(\gamma \)-spirallikeness of order \(\alpha \) of some special functions. Complex Anal Synerg 9, 14 (2023). https://doi.org/10.1007/s40627-023-00125-7

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