Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.a9we)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-5/2, a₂>=-5/2

For fixed z and a₁=-5/2, a₂=-1/2, a₃>=-1/2

For fixed z and a₁=-5/2, a₂=-1/2, a₃=2

For fixed z and a₁=-5/2, a₂=-1/2, a₃=2, b₁=5/2

http://functions.wolfram.com/07.27.03.a9we.01

Input Form

HypergeometricPFQ[{-(5/2), -(1/2), 2}, {5/2, 4}, z] == (8 (-4 + 77 z))/(8085 z^3) + (Sqrt[1 - z] (4096 - 76800 z + 83387 z^2 + 699362 z^3 + 59640 z^4 - 3920 z^5))/(1034880 z^3) + (3 (-35 + 112 z + 144 z^2) ArcSin[Sqrt[z]])/ (896 z^(3/2))

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},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},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]