Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b665)

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=-41/8

http://functions.wolfram.com/07.23.03.b665.01

Input Form

Hypergeometric2F1[-(45/8), -(41/8), 19/4, z] == (1/(23052384890643 z^4)) (8 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (-967846 + 29343331 z - 553607912 z^2 + 12468496060 z^3 + 645046738092 z^4 + 3027422039034 z^5 + 4205935857976 z^6 + 2003169874508 z^7 + 302316432170 z^8 + 9813396251 z^9) + (1/Sqrt[1 - z]) (3871384 - 119309016 z + 2272634387 z^2 - 50966770360 z^3 - 1114745523932 z^4 - 2699661515064 z^5 + 48839313554 z^6 + 2601646216632 z^7 + 1108800571180 z^8 + 102857455504 z^9 + 1073055731 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]