Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.blq4)

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=23/8

http://functions.wolfram.com/07.23.03.blq4.01

Input Form

Hypergeometric2F1[-(21/8), 23/8, -(21/4), z] == (1/(3264 2^(1/4) (-1 + z)^5)) ((1 + Sqrt[1 - z])^(1/4) (-1632 + 5712 z - 6006 z^2 + 735 z^3 + 740 z^4 + 1011 z^5 - 2096 z^6 + 768 z^7 + (2 (-816 + 3264 z - 4329 z^2 + 1563 z^3 + 415 z^4 + 373 z^5 + 4778 z^6 - 5248 z^7 + 1536 z^8))/Sqrt[1 - z]))

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]