Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c3po)

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=11/8, b>=a

For fixed z and a=11/8, b=39/8

http://functions.wolfram.com/07.23.03.c3po.01

Input Form

Hypergeometric2F1[11/8, 39/8, -(21/4), z] == (1/(5430208 2^(1/4) (-1 + z)^11)) ((1 + Sqrt[1 - z])^(1/4) (-2715104 + 33163056 z - 191139614 z^2 + 703529221 z^3 - 1941538215 z^4 + 4939882178 z^5 + 22021922868 z^6 + 579893193 z^7 - 68413407 z^8 + 4549520 z^9 + (1/Sqrt[1 - z]) (2 (-1357552 + 17260304 z - 103690877 z^2 + 397561670 z^3 - 1135688503 z^4 + 2916717584 z^5 - 42648078363 z^6 - 12720116706 z^7 + 1253108415 z^8 - 143082404 z^9 + 9099040 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]