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

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=4, a₃>=4

For fixed z and a₁=7/2, a₂=4, a₃=4

For fixed z and a₁=7/2, a₂=4, a₃=4, b₁=-5/2

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

Input Form

HypergeometricPFQ[{7/2, 4, 4}, {-(5/2), -(5/2)}, -z] == (1/(6400 (1 + z)^16)) (6400 + 45056 z + 1284096 z^2 - 358830080 z^3 + 108042833920 z^4 - 2786449863680 z^5 + 19593911858304 z^6 - 51005315136256 z^7 + 54925919751560 z^8 - 24850472075000 z^9 + 4414704729435 z^10 - 253448747552 z^11 + 2760906148 z^12) - (9009 (-146432 z^(7/2) + 10396672 z^(9/2) - 143940992 z^(11/2) + 667523072 z^(13/2) - 1254363032 z^(15/2) + 1021350616 z^(17/2) - 357232161 z^(19/2) + 49195146 z^(21/2) - 2138136 z^(23/2) + 16016 z^(25/2)) ArcSinh[Sqrt[z]])/(1280 Sqrt[1 + z] (1 + 16 z + 120 z^2 + 560 z^3 + 1820 z^4 + 4368 z^5 + 8008 z^6 + 11440 z^7 + 12870 z^8 + 11440 z^9 + 8008 z^10 + 4368 z^11 + 1820 z^12 + 560 z^13 + 120 z^14 + 16 z^15 + z^16))

Standard Form

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MathML Form

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</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]