The First Kind

AiryAi ${\rm AiryAi}(z)$ --- note this is the single-variable case

• Sage: https://doc.sagemath.org/html/en/reference/functions/sage/functions/airy.html
  • For numerical values using Arb see paper of Frederik Johansson

This module implements Airy functions and their generalized derivatives. It supports symbolic functionality through Maxima and numeric evaluation through mpmath and scipy.

Airy functions are solutions to the differential equation f″(x)−xf(x)=0

Four global function symbols are immediately available, please see
    airy_ai(): for the Airy Ai function
    airy_ai_prime(): for the first differential of the Airy Ai function
    airy_bi(): for the Airy Bi function

    airy_bi_prime(): for the first differential
        of the Airy Bi function

• http://dlmf.nist.gov/9
• http://en.wikipedia.org/wiki/Airy_function
• http://www.encyclopediaofmath.org/index.php/Airy_functions
• http://mathworld.wolfram.com/AiryFunctions.html

Airy Rough Notes

Bruce Miller, Cataloging DLMF’s Special Functions SS , JMM 2018

DLMF_AI

• defines
  • ScorerGi
    • parameters null
    • definitionurl "http://dlmf.nist.gov/9.12.E4"
    • signature "{\\Complexes\\mapsto\\Complexes}"
    • arguments "{z}"
    • description "{the Scorer (or inhomogeneous Airy) function $\\ScorerGi$}"
  • ScorerHi
    • parameters null
    • definitionurl "http://dlmf.nist.gov/9.12.E5"
    • signature "{\\Complexes\\mapsto\\Complexes}"
    • arguments "{z}"
    • description "{the Scorer (or inhomogeneous Airy) function $\\ScorerHi$}"
  • AiryBi
    • parameters null
    • equiv "airy:Bi"
    • definitionurl "http://dlmf.nist.gov/9.2.SS1"
    • signature "{\\Complexes\\mapsto\\Complexes}"
    • arguments "{z}"
    • description "{the Airy function $\\AiryBi$}"
  • AiryAi
    • parameters null
    • equiv "airy:Ai"
    • definitionurl "http://dlmf.nist.gov/9.2.SS1"
    • signature "{\\Complexes\\mapsto\\Complexes}"
    • arguments "{z}"
    • description "{the Airy function $\\AiryAi$}"
    • date "2018-08-09"
  • version "0"
  • status "experimental"
  • description "Definitions from Airy and Rel