Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.att3)

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=2, a₂>=2

For fixed z and a₁=2, a₂=7/2, a₃>=7/2

For fixed z and a₁=2, a₂=7/2, a₃=4

For fixed z and a₁=2, a₂=7/2, a₃=4, b₁=-7/2

http://functions.wolfram.com/07.27.03.att3.01

Input Form

HypergeometricPFQ[{2, 7/2, 4}, {-(7/2), -(5/2)}, z] == (1/(160 (-1 + z)^15)) (-160 + 1888 z - 13728 z^2 - 182176 z^3 + 65087200 z^4 + 4447722720 z^5 + 45670028768 z^6 + 142545131872 z^7 + 163088681184 z^8 + 70254773160 z^9 + 10273872180 z^10 + 358832529 z^11 + 354816 z^12 + 2772 z^13) + (9009 (11264 z^(9/2) + 278016 z^(11/2) + 1692288 z^(13/2) + 3615040 z^(15/2) + 3016728 z^(17/2) + 972972 z^(19/2) + 105963 z^(21/2) + 2574 z^(23/2)) ArcSin[Sqrt[z]])/ (32 Sqrt[1 - z] (-1 + 15 z - 105 z^2 + 455 z^3 - 1365 z^4 + 3003 z^5 - 5005 z^6 + 6435 z^7 - 6435 z^8 + 5005 z^9 - 3003 z^10 + 1365 z^11 - 455 z^12 + 105 z^13 - 15 z^14 + z^15))

Standard Form

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MathML Form

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<cn type='integer'> 15 </cn> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]