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. Axioms2024, 13, 134.
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.
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. Axioms2024, 13, 134.
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.
Abstract
The Bessel function of the first kind J_N(kx) is expanded in a Fourier-Legendre series, as is the modified Bessel functions of the first kind I_N(kx) . Known polynomial approximations for the range −3≤x≤3 (having five-digit accuracy) are compared with those arising from this Legendre series and substitute versions are given with twice the number of terms and range (with five-digit accuracy or having fifteen-digit accuracy over −3≤x≤3). It is shown that infinite series of like-powered contributors (involving _2F_3 hypergeometric functions) extracted from the Fourier-Legendre series may be summed, having values that are inverse powers of the first five primes 1/(2^i 3^j 5^k 7^l 11^mm) for powers of order x24.
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
