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

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=-39/8, b>=a

For fixed z and a=-39/8, b=45/8

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

Input Form

Hypergeometric2F1[-(39/8), 45/8, -(19/4), z] == (1/(50233568 2^(3/4) (-1 + z)^5)) ((1 + Sqrt[1 - z])^(3/4) (-25116784 - 24125332 z - 28339003 z^2 - 43308426 z^3 - 102212907 z^4 + 15126975732 z^5 - 49805336064 z^6 + 64091157504 z^7 - 37537775616 z^8 + 8382578688 z^9 + (1/Sqrt[1 - z]) (-25116784 - 11566940 z - 13136739 z^2 - 24553459 z^3 - 74527361 z^4 - 16179727149 z^5 + 74795363280 z^6 - 137925013248 z^7 + 127832702976 z^8 - 59597193216 z^9 + 11176771584 z^10)))

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]