Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ba09)

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=-39/8, b>=a

For fixed z and a=-39/8, b=-3/8

http://functions.wolfram.com/07.23.03.ba09.01

Input Form

Hypergeometric2F1[-(39/8), -(3/8), 21/4, z] == (1/(164444294245 z^5)) (16 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (1334736 - 17582580 z + 116621845 z^2 - 586186533 z^3 + 5731968138 z^4 + 6350777026 z^5 - 517502535 z^6 + 114123207 z^7 - 18223832 z^8 + 1442112 z^9 + (1/Sqrt[1 - z]) (-1334736 + 18249948 z - 125246293 z^2 + 642383054 z^3 - 6011530447 z^4 + 1587456464 z^5 + 4560384125 z^6 - 819199018 z^7 + 172854935 z^8 - 25940848 z^9 + 1922816 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]