Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8556)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 3 and fixed z

For fixed z and a=10/3, b>=a

For fixed z and a=10/3, b=11/3

http://functions.wolfram.com/07.23.03.8556.01

Input Form

Hypergeometric2F1[10/3, 11/3, -(7/2), z] == (1/(6967296 (-1 + z)^10)) ((1/Sqrt[1 - z]) ((6967296 - 97873920 z + 706654208 z^2 - 3929411584 z^3 + 31287517184 z^4 + 125716201369 z^5 + 62759413180 z^6 + 4471087408 z^7) Cos[ArcSin[Sqrt[z]]/3]) - 3 Sqrt[z] (-774144 + 10330112 z - 71307264 z^2 + 387186688 z^3 + 12616515481 z^4 + 10496252052 z^5 + 1108525424 z^6) Sin[ArcSin[Sqrt[z]]/3])

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]