Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5e6)

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=-47/8, b>=a

For fixed z and a=-47/8, b=23/8

http://functions.wolfram.com/07.23.03.b5e6.01

Input Form

Hypergeometric2F1[-(47/8), 23/8, 11/2, -z] == (1024 (Sqrt[z] Sqrt[1 + z] (15012928 + 69970968 z + 74494953 z^2 - 67960308 z^3 + 3983855878 z^4 + 13153055916 z^5 + 20100048617 z^6 + 17715881656 z^7 + 9303044784 z^8 + 2721761856 z^9 + 343335168 z^10) Cosh[ArcSinh[Sqrt[z]]/4] - (60051712 + 321169424 z + 485473857 z^2 - 87564243 z^3 + 1048157058 z^4 + 8859102298 z^5 + 21473104565 z^6 + 27951807433 z^7 + 22048642264 z^8 + 10621008816 z^9 + 2893429440 z^10 + 343335168 z^11) Sinh[ArcSinh[Sqrt[z]]/4]))/ (3759497784075 z^(9/2) Sqrt[1 + z])

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]