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gptkb:A001157
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1/sqrt(1-4x)
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gptkb:complete_Bell_polynomials
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exp(sum_{k=1}^∞ x_k t^k / k!)
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gptkb:Gegenbauer_polynomials
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(1-2xt+t^2)^{-λ} = \\sum_{n=0}^\\infty C_n^{(λ)}(x)t^n
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gptkb:physicists'_Hermite_polynomials
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exp(2xt - t^2) = sum_{n=0}^∞ H_n(x) t^n / n!
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gptkb:Chebyshev_T
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(1 - xt)/(1 - 2xt + t²)
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gptkb:Schröder's_number
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(1 - x - sqrt(1 - 6x + x^2)) / (2x)
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gptkb:Legendre_polynomial
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(1-2xt+t^2)^{-1/2} = \\sum_{n=0}^\\infty P_n(x)t^n
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gptkb:large_Schröder_numbers
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(1-x-sqrt(1-6x+x^2))/(2x)
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gptkb:A002117
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1/sqrt(1-4x)
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gptkb:Bell_numbers
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exp(exp(x)-1)
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gptkb:Schröder_number
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(1-x-sqrt(1-6x+x^2))/(2x)
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gptkb:Charlier_polynomials
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e^{-a t}(1+t)^x = \\sum_{n=0}^\\infty C_n(x;a) \\frac{t^n}{n!}
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gptkb:Stirling_numbers_of_the_second_kind
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sum_{n=0}^{∞} S(n, k) * x^n / n! = (e^{x} - 1)^k / k!
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gptkb:OEIS_A001349
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1/sqrt(1-4x)
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gptkb:small_Schröder_number
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(1-x-sqrt(1-6x+x^2))/(2x)
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gptkb:Catalan_numbers
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C(x) = (1 - sqrt(1-4x)) / (2x)
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gptkb:Hermite_polynomials
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exp(2xt-t^2) = sum_{n=0}^∞ H_n(x) t^n / n!
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gptkb:OEIS_A001097
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1/sqrt(1-4x)
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gptkb:probabilists'_Hermite_polynomials
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e^{xt - t^2/2} = \\sum_{n=0}^\\infty H_n(x) \\frac{t^n}{n!}
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gptkb:Hermite_polynomial
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exp(2xt - t^2) = sum_{n=0}^∞ H_n(x) t^n / n!
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