Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bek4)

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=-33/8, b>=a

For fixed z and a=-33/8, b=43/8

http://functions.wolfram.com/07.23.03.bek4.01

Input Form

Hypergeometric2F1[-(33/8), 43/8, -(11/2), z] == (1/9805824) ((1/(1 - Sqrt[z])^(27/4)) (4902912 - 33094656 Sqrt[z] + 114912000 z - 284062464 z^(3/2) + 568546272 z^2 - 980299908 z^(5/2) + 1506336207 z^3 - 2100642660 z^(7/2) + 2680289568 z^4 - 3124687104 z^(9/2) + 3286483200 z^5 - 3011613696 z^(11/2) + 2230824960 z^6 - 1191051264 z^(13/2) + 391053312 z^7 - 57933824 z^(15/2)) + (1/(1 + Sqrt[z])^(27/4)) (4902912 + 33094656 Sqrt[z] + 114912000 z + 284062464 z^(3/2) + 568546272 z^2 + 980299908 z^(5/2) + 1506336207 z^3 + 2100642660 z^(7/2) + 2680289568 z^4 + 3124687104 z^(9/2) + 3286483200 z^5 + 3011613696 z^(11/2) + 2230824960 z^6 + 1191051264 z^(13/2) + 391053312 z^7 + 57933824 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]