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

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=-29/8, b>=a

For fixed z and a=-29/8, b=47/8

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

Input Form

Hypergeometric2F1[-(29/8), 47/8, -(11/2), z] == (1/192749568) ((1/(1 - Sqrt[z])^(31/4)) (96374784 - 746904576 Sqrt[z] + 2893981440 z - 7723672320 z^(3/2) + 16246703200 z^2 - 28810906852 z^(5/2) + 44673308043 z^3 - 61737657540 z^(7/2) + 76591600800 z^4 - 84960395520 z^(9/2) + 82767869184 z^5 - 67968316416 z^(11/2) + 43850526720 z^6 - 20134625280 z^(13/2) + 5698682880 z^7 - 735313920 z^(15/2)) + (1/(1 + Sqrt[z])^(31/4)) (96374784 + 746904576 Sqrt[z] + 2893981440 z + 7723672320 z^(3/2) + 16246703200 z^2 + 28810906852 z^(5/2) + 44673308043 z^3 + 61737657540 z^(7/2) + 76591600800 z^4 + 84960395520 z^(9/2) + 82767869184 z^5 + 67968316416 z^(11/2) + 43850526720 z^6 + 20134625280 z^(13/2) + 5698682880 z^7 + 735313920 z^(15/2)))

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]