On Some Branched Continued Fraction Expansions for Horn’s Hypergeometric Function H4(a,b;c,d;z1,z2) Ratios
Abstract
:1. Introduction
- (i)
- To construct the BCFE;
- (ii)
- To prove the convergence of the constructed expansion;
- (iii)
- To prove the convergence of the BCF to the function of which it is an expansion.
2. Expansions
3. Convergence of BCFE for
4. Numerical Experiments
5. Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
BCF | Branched continued fraction |
BCFE | Branched continued fraction expansion |
FBCFE | Formal branched continued fraction expansion |
DPS | Double power series |
FDPS | Formal double power series |
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Antonova, T.; Dmytryshyn, R.; Lutsiv, I.-A.; Sharyn, S. On Some Branched Continued Fraction Expansions for Horn’s Hypergeometric Function H4(a,b;c,d;z1,z2) Ratios. Axioms 2023, 12, 299. https://doi.org/10.3390/axioms12030299
Antonova T, Dmytryshyn R, Lutsiv I-A, Sharyn S. On Some Branched Continued Fraction Expansions for Horn’s Hypergeometric Function H4(a,b;c,d;z1,z2) Ratios. Axioms. 2023; 12(3):299. https://doi.org/10.3390/axioms12030299
Chicago/Turabian StyleAntonova, Tamara, Roman Dmytryshyn, Ilona-Anna Lutsiv, and Serhii Sharyn. 2023. "On Some Branched Continued Fraction Expansions for Horn’s Hypergeometric Function H4(a,b;c,d;z1,z2) Ratios" Axioms 12, no. 3: 299. https://doi.org/10.3390/axioms12030299