Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bm1c)

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=-21/8, b>=a

For fixed z and a=-21/8, b=39/8

http://functions.wolfram.com/07.23.03.bm1c.01

Input Form

Hypergeometric2F1[-(21/8), 39/8, -(9/4), z] == (1/(85560 2^(1/4) (-1 + z)^4)) ((1 + Sqrt[1 - z])^(1/4) (42780 + 74865 z + 218178 z^2 - 3780719 z^3 + 7969248 z^4 - 6310656 z^5 + 1757184 z^6 + (1/Sqrt[1 - z]) (42780 + 53475 z + 175398 z^2 + 9481867 z^3 - 35245616 z^4 + 48654720 z^5 - 30074880 z^6 + 7028736 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]