Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.ate6)

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=5/2, a₃>=5/2

For fixed z and a₁=2, a₂=5/2, a₃=7/2

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

http://functions.wolfram.com/07.27.03.ate6.01

Input Form

HypergeometricPFQ[{2, 5/2, 7/2}, {-(5/2), -(5/2)}, z] == (1/(5 (1 - z)^2 (-1 + z)^11)) (-5 + 51 z - 355 z^2 - 17155 z^3 - 3227250 z^4 - 46565090 z^5 - 165888294 z^6 - 189459270 z^7 - 71576505 z^8 - 7596225 z^9 - 112455 z^10 + 441 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]