Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c2sa)

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=9/8, b>=a

For fixed z and a=9/8, b=45/8

http://functions.wolfram.com/07.23.03.c2sa.01

Input Form

Hypergeometric2F1[9/8, 45/8, -(19/4), z] == ((1 + Sqrt[1 - z])^(3/4) (-25116784 + 305036732 z - 1756439839 z^2 + 6543049919 z^3 - 19039807726 z^4 - 675124399558 z^5 - 18355348651 z^6 + 3863047547 z^7 - 591670216 z^8 + 45038784 z^9 + (1/Sqrt[1 - z]) (-25116784 + 317595124 z - 1905818607 z^2 + 7384710046 z^3 - 22109861377 z^4 + 807907464984 z^5 + 171085484383 z^6 - 28848078394 z^7 + 5822569761 z^8 - 840187792 z^9 + 60051712 z^10)))/(50233568 2^(3/4) (-1 + z)^11)

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]