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

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=7/2, a₃>=7/2

For fixed z and a₁=5/2, a₂=7/2, a₃=4

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

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

Input Form

HypergeometricPFQ[{5/2, 7/2, 4}, {-(5/2), -(3/2)}, z] == (1/(3 (1 - z)^4 (-1 + z)^10)) (3 - 14 z + 1351 z^2 - 310184 z^3 - 20077834 z^4 - 192098452 z^5 - 550944394 z^6 - 568809384 z^7 - 215143929 z^8 - 26360334 z^9 - 693693 z^10)

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]