generatingFunction

23 triples
GPTKB property

Random triples
Subject Object
gptkb:generalized_Laguerre_polynomials (1-t)^{-α-1} exp(-xt/(1-t)) = Σ_{n=0}^∞ L_n^{(α)}(x) t^n
gptkb:large_Schröder_numbers (1-x-sqrt(1-6x+x^2))/(2x)
gptkb:Gegenbauer_polynomials (1-2xt+t^2)^{-λ} = \\sum_{n=0}^\\infty C_n^{(λ)}(x)t^n
gptkb:Schröder's_number (1 - x - sqrt(1 - 6x + x^2)) / (2x)
gptkb:Bell_numbers exp(exp(x)-1)
gptkb:complete_Bell_polynomials exp(sum_{k=1}^∞ x_k t^k / k!)
gptkb:OEIS_A001349 1/sqrt(1-4x)
gptkb:Hermite_polynomial exp(2xt - t^2) = sum_{n=0}^∞ H_n(x) t^n / n!
gptkb:Schröder_number (1-x-sqrt(1-6x+x^2))/(2x)
gptkb:OEIS_A001097 1/sqrt(1-4x)
gptkb:Euler_polynomials 2e^{xt}/(e^t+1) = sum_{n=0}^∞ E_n(x) t^n/n!
gptkb:Chebyshev_T (1 - xt)/(1 - 2xt + t²)
gptkb:Stirling_numbers_of_the_second_kind sum_{n=0}^{∞} S(n, k) * x^n / n! = (e^{x} - 1)^k / k!
gptkb:Legendre_polynomial (1-2xt+t^2)^{-1/2} = \\sum_{n=0}^\\infty P_n(x)t^n
gptkb:Bernoulli_numbers x/(e^x - 1)
gptkb:A001157 1/sqrt(1-4x)
gptkb:Hermite_polynomials exp(2xt-t^2) = sum_{n=0}^∞ H_n(x) t^n / n!
gptkb:small_Schröder_number (1-x-sqrt(1-6x+x^2))/(2x)
gptkb:physicists'_Hermite_polynomials exp(2xt - t^2) = sum_{n=0}^∞ H_n(x) t^n / n!
gptkb:Catalan_numbers C(x) = (1 - sqrt(1-4x)) / (2x)