Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bb6u)

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=-37/8, b>=a

For fixed z and a=-37/8, b=-35/8

http://functions.wolfram.com/07.23.03.bb6u.01

Input Form

Hypergeometric2F1[-(37/8), -(35/8), 9/2, z] == (1/(1052123587515 z^(7/2))) (256 (Sqrt[z] (-154512 + 3943275 z - 64286649 z^2 + 5654281743 z^3 + 36785788747 z^4 + 57723619473 z^5 + 27462233541 z^6 + 3562734133 z^7 + 69669369 z^8) Cos[(3 ArcSin[Sqrt[z]])/4] + (1/Sqrt[1 - z]) ((206016 - 5433672 z + 90199599 z^2 - 2132275257 z^3 - 21110248773 z^4 - 22155630477 z^5 + 20849993645 z^6 + 21035763029 z^7 + 3357756521 z^8 + 69669369 z^9) Sin[(3 ArcSin[Sqrt[z]])/4])))

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]