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

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=3/2, a₂>=3/2

For fixed z and a₁=3/2, a₂=7/2, a₃>=7/2

For fixed z and a₁=3/2, a₂=7/2, a₃=4

For fixed z and a₁=3/2, a₂=7/2, a₃=4, b₁=-7/2

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

Input Form

HypergeometricPFQ[{3/2, 7/2, 4}, {-(7/2), -(7/2)}, z] == (1/(7 (1 - z)^4 (-1 + z)^12)) (7 - 100 z + 702 z^2 - 2420 z^3 + 186905 z^4 + 46990776 z^5 + 1062826660 z^6 + 6414644600 z^7 + 13904424105 z^8 + 11913252780 z^9 + 3979825278 z^10 + 452740860 z^11 + 11594583 z^12)

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]