Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b68m)

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=-33/8

http://functions.wolfram.com/07.23.03.b68m.01

Input Form

Hypergeometric2F1[-(45/8), -(33/8), 19/4, z] == (1/(324681477333 z^4)) (8 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-94424 + 2540864 z - 41858803 z^2 + 805613765 z^3 + 35054593953 z^4 + 131792100441 z^5 + 137394525959 z^6 + 43624232527 z^7 + 3287597155 z^8 - 368621 z^9 - (1/Sqrt[1 - z]) (4 (-23606 + 647019 z - 10779358 z^2 + 206557865 z^3 + 3591067993 z^4 + 5979496731 z^5 - 2872617091 z^6 - 5573387853 z^7 - 1282256495 z^8 - 39073826 z^9 + 368621 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]