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

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=27/8, b>=a

For fixed z and a=27/8, b=47/8

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

Input Form

Hypergeometric2F1[27/8, 47/8, -(21/4), z] == (1/(3069248 2^(1/4) (-1 + z)^14)) ((1 + Sqrt[1 - z])^(1/4) (2 (767312 - 13592384 z + 119818751 z^2 - 723897957 z^3 + 3616448437 z^4 - 19188647933 z^5 - 379632297397 z^6 - 417727424487 z^7 - 84631729521 z^8 - 246299639 z^9 + 6938018 z^10) + (1/Sqrt[1 - z]) (1534624 - 27952080 z + 253038058 z^2 - 1564312483 z^3 + 7928479245 z^4 - 41826727215 z^5 + 1987978900613 z^6 + 3735987982119 z^7 + 1421782904151 z^8 + 78798539435 z^9 - 2008556211 z^10 + 55504144 z^11)))

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]