The Fourier–Legendre Series of Bessel Functions of the First Kind and the Summed Series Involving 1F2 Hypergeometric Functions That Arise from Them
Abstract
:1. Introduction
2. The Fourier–Legendre Series of a Bessel Function of the First Kind
3. A Numerical Check
4. Summing a Set of Infinite Series
5. Series Arising from the Fourier–Legendre Series
6. Series Arising from the Fourier–Legendre Series
7. Conclusions
Funding
Data Availability Statement
Conflicts of Interest
Correction Statement
Appendix A
References
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0.919730410089760239314421194080619970661964806513 |
0.998701439402686183101278177652801821334364120020 |
0.999990839756911599063652010604829164640891568430 |
0.999999963887689188843944699951660807338623340119 |
0.999999999909168357337955807722426205787682516277 |
0.999999999999841620300892054094280728854756176645 |
0.99999999999999979732605041136082528291421094660 |
0.999999999999999999801573588581204243621535893434 |
0.999999999999999999999846581786952424267000275450 |
0.999999999999999999999999903953851991585994488442 |
0.999999999999999999999999999950320420042897103088 |
0.999999999999999999999999999999978412290228685090 |
0.999999999999999999999999999999999992008312509362 |
0.999999999999999999999999999999999999997449396440 |
0.999999999999999999999999999999999999999999290955 |
0.999999999999999999999999999999999999999999999827 |
1.00000000000000000000000000000000000000000000000 |
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Straton, J.C. The Fourier–Legendre Series of Bessel Functions of the First Kind and the Summed Series Involving 1F2 Hypergeometric Functions That Arise from Them. Axioms 2024, 13, 134. https://doi.org/10.3390/axioms13020134
Straton JC. The Fourier–Legendre Series of Bessel Functions of the First Kind and the Summed Series Involving 1F2 Hypergeometric Functions That Arise from Them. Axioms. 2024; 13(2):134. https://doi.org/10.3390/axioms13020134
Chicago/Turabian StyleStraton, Jack C. 2024. "The Fourier–Legendre Series of Bessel Functions of the First Kind and the Summed Series Involving 1F2 Hypergeometric Functions That Arise from Them" Axioms 13, no. 2: 134. https://doi.org/10.3390/axioms13020134