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

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=-37/8, b>=a

For fixed z and a=-37/8, b=47/8

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

Input Form

Hypergeometric2F1[-(37/8), 47/8, -(9/4), z] == (1/(51336 2^(1/4) (-1 + z)^3)) ((1 + Sqrt[1 - z])^(1/4) (-25668 - 234577 z - 2252367 z^2 + 140636148 z^3 - 657590784 z^4 + 1157870592 z^5 - 892403712 z^6 + 254017536 z^7 + (1/Sqrt[1 - z]) (-25668 - 221743 z - 2131870 z^2 - 293379999 z^3 + 2107414128 z^4 - 5561873664 z^5 + 7002243072 z^6 - 4268163072 z^7 + 1016070144 z^8)))

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]