ordinaryHypergeometricCoefficient

English

The nth coefficient of the ordinary hypergeometric series is given by (n!^{-1}) · (ascPochhammer n).eval(a) · (ascPochhammer n).eval(b) · ((ascPochhammer n).eval(c))^{-1}.

Русский

n-й коэффициент обыкновенного гипергеометрического ряда равен (n!^{-1}) · (ascPochhammer n).eval(a) · (ascPochhammer n).eval(b) · ((ascPochhammer n).eval(c))^{-1}.

LaTeX

$$$\\displaystyle \\text{coeff}(n) = (n!^{-1}) \\cdot (\\mathrm{ascPochhammer}\\;\\mathbb{K}\\;n).\\mathrm{eval}(a) \\cdot (\\mathrm{ascPochhammer}\\;\\mathbb{K}\\;n).\\mathrm{eval}(b) \\cdot (\\mathrm{ascPochhammer}\\;\\mathbb{K}\\;n).\\mathrm{eval}(c)^{-1}$$$

Lean4

/-- The coefficients in the ordinary hypergeometric sum. -/
noncomputable abbrev ordinaryHypergeometricCoefficient (a b c : 𝕂) (n : ℕ) :=
  ((n !⁻¹ : 𝕂) * (ascPochhammer 𝕂 n).eval a * (ascPochhammer 𝕂 n).eval b * ((ascPochhammer 𝕂 n).eval c)⁻¹)

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