Notes

Chapter 4: Systems Based on Numbers

Section 6: Mathematical Functions


Mathematical functions

(See page 1091.) BesselJ[0, x] goes like Sin[x]/Sqrt[x] for large x while AiryAi[-x] goes like Sin[x3/2]/x1/4. Other standard mathematical functions that oscillate at large x include JacobiSN and MathieuC. Most hypergeometric-type functions either increase or decrease exponentially for large arguments, though in the directions of Stokes lines in the complex plane they can oscillate sinusoidally. (For AiryAi[x] the Stokes lines are in directions (-1)^({1, 2, 3}/3).)



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From Stephen Wolfram: A New Kind of Science [citation]