Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.cax5)

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=33/8

http://functions.wolfram.com/07.23.03.cax5.01

Input Form

Hypergeometric2F1[29/8, 33/8, -(23/4), z] == (-27968 + 438064 z - 3335160 z^2 + 16784555 z^3 - 65533338 z^4 + 234850629 z^5 - 1144379652 z^6 - 4311079803 z^7 - 1925654922 z^8 - 133705797 z^9 + (1/Sqrt[1 - z]) (-27968 + 452048 z - 3550696 z^2 + 18399125 z^3 - 73535007 z^4 + 265711329 z^5 - 1254543459 z^6 - 14617235889 z^7 - 11804899437 z^8 - 1828277205 z^9 - 29066409 z^10))/ (27968 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-1 + z)^13)

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]