Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b71v)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a<0

For fixed z and a=-45/8, b>=a

For fixed z and a=-45/8, b=31/8

http://functions.wolfram.com/07.23.03.b71v.01

Input Form

Hypergeometric2F1[-(45/8), 31/8, 19/4, z] == (1/(18941609865 z^4)) (8 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (8592584 + 3124576 z + 9443473 z^2 + 67861885 z^3 - 780445749 z^4 + 2256714783 z^5 - 3162895648 z^6 + 2409062656 z^7 - 963522560 z^8 + 159318016 z^9 + (1/Sqrt[1 - z]) (4 (-2148146 + 292929 z - 1701778 z^2 - 15553135 z^3 + 499984669 z^4 - 2146978686 z^5 + 4267812883 z^6 - 4746388416 z^7 + 3058415360 z^8 - 1073053696 z^9 + 159318016 z^10))))

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]