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Stieltjes–Wigert polynomials

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1: 18.27 q -Hahn Class
§18.27(vi) StieltjesWigert Polynomials
18.27.18 S n ( x ; q ) = = 0 n q 2 ( - x ) ( q ; q ) ( q ; q ) n - = 1 ( q ; q ) n ϕ 1 1 ( q - n 0 ; q , - q n + 1 x ) .
2: 18.1 Notation
  • StieltjesWigert: S n ( x ; q ) .

  • 3: 18.29 Asymptotic Approximations for q -Hahn and Askey–Wilson Classes
    18.29.2 Q n ( z ; a , b , c , d q ) z n ( a z - 1 , b z - 1 , c z - 1 , d z - 1 ; q ) ( z - 2 , b c , b d , c d ; q ) , n ; z , a , b , c , d , q fixed.
    For a uniform asymptotic expansion of the StieltjesWigert polynomials, see Wang and Wong (2006). …
    4: Bibliography W
  • Z. Wang and R. Wong (2006) Uniform asymptotics of the Stieltjes-Wigert polynomials via the Riemann-Hilbert approach. J. Math. Pures Appl. (9) 85 (5), pp. 698–718.