Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.1766)

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=-7/2, a₂>=-7/2

For fixed z and a₁=-7/2, a₂=-7/2, a₃>=-7/2

For fixed z and a₁=-7/2, a₂=-7/2, a₃=2

For fixed z and a₁=-7/2, a₂=-7/2, a₃=2, b₁=5/2

http://functions.wolfram.com/07.27.03.1766.01

Input Form

HypergeometricPFQ[{-(7/2), -(7/2), 2}, {5/2, 4}, z] == (8 (-4 + 169 z))/(184041 z^3) + (1/(7538319360 z^3)) (Sqrt[1 - z] (1310720 - 54722560 z + 108072695 z^2 + 6255440980 z^3 + 12115771684 z^4 + 4790858752 z^5 + 309865824 z^6)) + (7 (-3003 + 30030 z + 205920 z^2 + 228800 z^3 + 58240 z^4 + 2304 z^5) ArcSin[Sqrt[z]])/(1171456 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]