Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c6jr)

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=37/8

http://functions.wolfram.com/07.23.03.c6jr.01

Input Form

Hypergeometric2F1[17/8, 37/8, -(23/4), z] == (1/(811072 2^(3/4) (-1 + z)^12)) ((1 + Sqrt[1 - z])^(3/4) (2 (202768 - 2741776 z + 17679531 z^2 - 73560588 z^3 + 230239149 z^4 - 636144174 z^5 - 31837186107 z^6 - 14395189968 z^7 - 44335053 z^8 + 1809594 z^9) + (1/Sqrt[1 - z]) (405536 - 5686320 z + 38050146 z^2 - 164140609 z^3 + 529945884 z^4 - 1486144179 z^5 + 73415065170 z^6 + 49416800697 z^7 + 3011164416 z^8 - 122348661 z^9 + 4825584 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]