hasSeriesExpansion

20 triples
GPTKB property

Random triples
Subject Object
gptkb:Weierstrass_℘-function gptkb:Laurent_series
gptkb:Lerch_zeta_function Σ_{n=0}^∞ z^n / (n+a)^s
gptkb:modified_Bessel_function_of_the_first_kind,_order_1 I₁(x) = Σ_{k=0}^∞ [ (x/2)^{2k+1} / (k! Γ(k+2)) ]
gptkb:Airy_function_Bi(x) yes
gptkb:Weierstrass_elliptic_function gptkb:Laurent_series
gptkb:Complete_elliptic_integral_of_the_second_kind E(k) = (π/2) [1 - (1/4)k^2 - (3/64)k^4 - (5/256)k^6 - ...]
gptkb:modified_Bessel_function_of_the_second_kind yes
gptkb:logarithmic_integral yes
gptkb:Kummer_function sum_{n=0}^∞ (a)_n z^n / [(b)_n n!]
gptkb:Lerch_transcendent Σ_{n=0}^∞ z^n / (n + a)^s
gptkb:Complete_elliptic_integral_of_the_first_kind K(k) = (π/2) Σ_{n=0}^∞ [(2n)!/(2^n n!)^2] k^{2n}
gptkb:Digamma_function ψ(x) = ln(x) - 1/(2x) - ∑_{k=1}^∞ B_{2k}/(2k x^{2k})
gptkb:Euler_Z ζ(s) = 1 + 1/2^s + 1/3^s + ...
gptkb:The_Logarithmic_Integral_II li₂(x) = Σ_{k=1}^∞ x^k / k^2
gptkb:parabolic_cylinder_function yes
gptkb:Hurwitzsche_Zeta-Funktion Laurent series at s=1
gptkb:Jacobi_theta_function Fourier series
gptkb:Lambert_W_function Maclaurin series at x=0
gptkb:Weierstrass_elliptic_functions gptkb:Laurent_series
gptkb:Kummer's_function sum_{n=0}^∞ [(a)_n / (b)_n] * z^n / n!