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

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=-37/8, b>=a

For fixed z and a=-37/8, b=-25/8

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

Input Form

Hypergeometric2F1[-(37/8), -(25/8), 19/4, z] == (1/(324681477333 z^4)) (8 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-300440 + 6309240 z - 78259255 z^2 + 1080350050 z^3 + 32483709559 z^4 + 75170590324 z^5 + 40689891591 z^6 + 4613057938 z^7 - 837775 z^8 - (1/Sqrt[1 - z]) (4 (-75110 + 1614865 z - 20344080 z^2 + 279677450 z^3 + 2915085504 z^4 + 1482700392 z^5 - 3177699064 z^6 - 1416451282 z^7 - 65346450 z^8 + 837775 z^9))))

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]