Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bb9m)

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=-27/8

http://functions.wolfram.com/07.23.03.bb9m.01

Input Form

Hypergeometric2F1[-(37/8), -(27/8), 11/2, z] == (1/(42669456604775 z^(9/2))) (1024 (-2 Sqrt[z] (-309024 + 6322116 z - 70428501 z^2 + 654367977 z^3 - 30632530333 z^4 - 132166236879 z^5 - 129885168279 z^6 - 34228525021 z^7 - 1682017623 z^8 + 9952767 z^9) Cos[(3 ArcSin[Sqrt[z]])/4] - (1/Sqrt[1 - z]) ((824064 - 17562864 z + 202182171 z^2 - 1904852907 z^3 + 27612076617 z^4 + 156874399113 z^5 + 34859377451 z^6 - 153705057409 z^7 - 60567303757 z^8 - 3373988013 z^9 + 19905534 z^10) Sin[(3 ArcSin[Sqrt[z]])/4])))

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]