Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.any4)

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=1/2, a₂>=1/2

For fixed z and a₁=1/2, a₂=2, a₃>=2

For fixed z and a₁=1/2, a₂=2, a₃=2

For fixed z and a₁=1/2, a₂=2, a₃=2, b₁=-7/2

http://functions.wolfram.com/07.27.03.any4.01

Input Form

HypergeometricPFQ[{1/2, 2, 2}, {-(7/2), -(7/2)}, z] == (1/(4900 (-1 + z)^11)) (-4900 + 53100 z - 261564 z^2 + 768884 z^3 - 1924200 z^4 - 46393320 z^5 - 411836920 z^6 - 728650296 z^7 - 316055124 z^8 - 23396835 z^9) - (99 (1408 z^(9/2) + 37888 z^(11/2) + 165088 z^(13/2) + 182688 z^(15/2) + 51513 z^(17/2) + 2310 z^(19/2)) ArcSin[Sqrt[z]])/ (140 Sqrt[1 - z] (-1 + 11 z - 55 z^2 + 165 z^3 - 330 z^4 + 462 z^5 - 462 z^6 + 330 z^7 - 165 z^8 + 55 z^9 - 11 z^10 + 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},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]