Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c6qo)

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=17/8, b>=a

For fixed z and a=17/8, b=45/8

http://functions.wolfram.com/07.23.03.c6qo.01

Input Form

Hypergeometric2F1[17/8, 45/8, -(7/4), z] == (1/(390572 2^(3/4) (-1 + z)^9)) ((1 + Sqrt[1 - z])^(3/4) (-195286 + 3054831 z + 1058620656 z^2 + 1313632898 z^3 + 16722702 z^4 - 2236681 z^5 + 171120 z^6 + (1/Sqrt[1 - z]) (2 (-97643 + 1576237 z - 566944730 z^2 - 922627806 z^3 - 116030055 z^4 + 12418321 z^5 - 1588564 z^6 + 114080 z^7))))

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]