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

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=5/2, a₃>=5/2

For fixed z and a₁=3/2, a₂=5/2, a₃=4

For fixed z and a₁=3/2, a₂=5/2, a₃=4, b₁=-7/2

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

Input Form

HypergeometricPFQ[{3/2, 5/2, 4}, {-(7/2), -(7/2)}, z] == (1/(49 (1 - z)^4 (-1 + z)^11)) (-49 + 675 z - 4455 z^2 + 16205 z^3 - 526890 z^4 - 109048002 z^5 - 2091953710 z^6 - 10385113830 z^7 - 17734218645 z^8 - 11189386065 z^9 - 2438727291 z^10 - 135270135 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]