Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c7nv)

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=19/8, b>=a

For fixed z and a=19/8, b=47/8

http://functions.wolfram.com/07.23.03.c7nv.01

Input Form

Hypergeometric2F1[19/8, 47/8, -(13/4), z] == (1/(148304 2^(1/4) (-1 + z)^11)) ((1 + Sqrt[1 - z])^(1/4) (-74152 + 1129392 z - 9152781 z^2 + 62334025 z^3 + 1286959590 z^4 + 1015947074 z^5 + 15072431 z^6 - 1471083 z^7 + 85840 z^8 + (1/Sqrt[1 - z]) (4 (-18538 + 291617 z - 2427052 z^2 + 16693469 z^3 - 853710980 z^4 - 1326897189 z^5 - 219394164 z^6 + 16076759 z^7 - 1530098 z^8 + 85840 z^9))))

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]