Infinite Series and Logarithmic Integrals Associated to Differentiation with Respect to Parameters of the Whittaker Wκ,μ(x) Function II
Abstract
:1. Introduction
2. Parameter Differentiation of via Kummer Function
2.1. Derivative with Respect to the First Parameter
2.2. Derivative with Respect to the Second Parameter
3. Parameter Differentiation of via Integral Representations
3.1. Derivative with Respect to the First Parameter
3.2. Application to the Calculation of Infinite Integrals
3.3. Derivative with Respect to the Second Parameter
4. Integral Whittaker Functions and
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Calculation of G(1) (a; a; z)
Appendix B. Calculation of 2F2 (1, 1; 2, 2 + m; x)
Appendix C. Reduction Formulas for the Whittaker Function Wκ,μ (x)
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Apelblat, A.; González-Santander, J.L. Infinite Series and Logarithmic Integrals Associated to Differentiation with Respect to Parameters of the Whittaker Wκ,μ(x) Function II. Axioms 2023, 12, 382. https://doi.org/10.3390/axioms12040382
Apelblat A, González-Santander JL. Infinite Series and Logarithmic Integrals Associated to Differentiation with Respect to Parameters of the Whittaker Wκ,μ(x) Function II. Axioms. 2023; 12(4):382. https://doi.org/10.3390/axioms12040382
Chicago/Turabian StyleApelblat, Alexander, and Juan Luis González-Santander. 2023. "Infinite Series and Logarithmic Integrals Associated to Differentiation with Respect to Parameters of the Whittaker Wκ,μ(x) Function II" Axioms 12, no. 4: 382. https://doi.org/10.3390/axioms12040382