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