inhomogeneous equations ♦ 21—21 of 21 matching pages ♦ SearchAdvancedHelp (0.000 seconds) 21—21 of 21 matching pages 21: 11.11 Asymptotic Expansions of Anger–Weber Functions … ► 11.11.9_5 a k + 1 ( λ ) = λ 1 − λ 2 λ a k ′′ ( λ ) + a k ′ ( λ ) ( 2 k + 1 ) ( 2 k + 2 ) , k = 0 , 1 , 2 , … . ⓘ Symbols: k : nonnegative integer, λ : parameter and a k ( λ ) : expansion function Referenced by: Erratum (V1.1.2) for Additions Permalink: http://dlmf.nist.gov/11.11.E9_5 Encodings: pMML, png, TeX Addition (effective with 1.1.2): This equation was added. See also: Annotations for §11.11(iii), §11.11 and Ch.11 … ► 11.11.13_5 ( 1 2 ) k b k ( λ ) = ( − 1 ) k ( 1 − λ 2 ) 1 / 4 U k ( 1 1 − λ 2 ) , k = 0 , 1 , 2 , … , ⓘ Symbols: ( a ) n : Pochhammer’s symbol (or shifted factorial), k : nonnegative integer, λ : parameter and b k ( λ ) : expansion function Referenced by: Erratum (V1.1.2) for Additions Permalink: http://dlmf.nist.gov/11.11.E13_5 Encodings: pMML, png, TeX Addition (effective with 1.1.2): This equation was added. See also: Annotations for §11.11(iii), §11.11 and Ch.11 … ► 11.11.17 𝐀 − ν ( ν + a ν 1 / 3 ) = 2 1 / 3 ν − 1 / 3 Hi ( − 2 1 / 3 a ) + O ( ν − 1 ) , ⓘ Symbols: O ( x ) : order not exceeding, Hi ( z ) : Scorer function (inhomogeneous Airy function), 𝐀 ν ( z ) : Anger–Weber function, ν : real or complex order and a k ( λ ) : expansion function Sources: Olver (1997b, pp. 103 and 352); Nemes (2020) Referenced by: §11.11(iii), §11.11(iii), §11.11(iii) Permalink: http://dlmf.nist.gov/11.11.E17 Encodings: pMML, png, TeX See also: Annotations for §11.11(iii), §11.11 and Ch.11 …