Amos, D. E. A portable package for Bessel functions of a complex argument and nonnegative order. (English) Zbl 0613.65013 ACM Trans. Math. Softw. 12, 265-273 (1986). This algorithm is a package of subroutines for computing Bessel functions \(H_ v^{(1)}(z)\), \(H_ v^{(2)}(z)\), \(I_ v(z)\), \(J_ v(z)\), \(K_ v(z)\), \(Y_ v(z)\) and Airy functions Ai(z), Ai’(z), Bi(z), Bi’(z) for orders \(v\geq 0\) and complex z in \(-\pi <\arg z\leq \pi\). Eight callable subroutines and their double-precision counterparts are provided. Exponential scaling and sequence generation are auxiliary options. Cited in 5 ReviewsCited in 37 Documents MSC: 65D20 Computation of special functions and constants, construction of tables 33-04 Software, source code, etc. for problems pertaining to special functions 33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\) Keywords:log gamma function; algorithm; package of subroutines; Bessel functions; Airy functions; Exponential scaling; sequence generation Software:Algorithm 644 PDFBibTeX XMLCite \textit{D. E. Amos}, ACM Trans. Math. Softw. 12, 265--273 (1986; Zbl 0613.65013) Full Text: DOI Link Digital Library of Mathematical Functions: In §10.77(v) Bessel Functions–Real Order and Complex Argument (including Hankel Functions) ‣ §10.77 Software ‣ Computation ‣ Chapter 10 Bessel Functions In §5.24(ii) Γ(𝑥), 𝑥∈ℝ ‣ §5.24 Software ‣ Computation ‣ Chapter 5 Gamma Function In §9.20(ii) Ai(𝑥), Ai’(𝑥), Bi(𝑥), Bi’(𝑥), 𝑥∈ℝ ‣ §9.20 Software ‣ Computation ‣ Chapter 9 Airy and Related Functions In §9.20(iii) Ai(𝑧), Ai’(𝑧), Bi(𝑧), Bi’(𝑧), 𝑧∈ℂ ‣ §9.20 Software ‣ Computation ‣ Chapter 9 Airy and Related Functions