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

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-17/4, b>=a

For fixed z and a=-17/4, b=23/4

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

Input Form

Hypergeometric2F1[-(17/4), 23/4, 4, z] == (1/(10548412875 Pi z^3)) (256 (2 (-21216 - 212823 z - 2492217 z^2 + 137869100 z^3 - 677376000 z^4 + 1255317504 z^5 - 1015021568 z^6 + 301989888 z^7) EllipticE[(1/2) (1 - Sqrt[1 - z])] + (21216 (1 + Sqrt[1 - z]) + 663 (321 + 329 Sqrt[1 - z]) z + 663 (3759 + 3845 Sqrt[1 - z]) z^2 - 100 (1378691 + 547952 Sqrt[1 - z]) z^3 + 358400 (1890 + 491 Sqrt[1 - z]) z^4 - 8192 (153237 + 24352 Sqrt[1 - z]) z^5 + 8388608 (121 + 9 Sqrt[1 - z]) z^6 - 301989888 z^7) EllipticK[(1/2) (1 - 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]