Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.3446)

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=-5/2, a₃>=-5/2

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

For fixed z and a₁=-7/2, a₂=-5/2, a₃=4, b₁=-1/2

http://functions.wolfram.com/07.27.03.3446.01

Input Form

HypergeometricPFQ[{-(7/2), -(5/2), 4}, {-(1/2), 5/2}, z] == (-105 + 60251 z - 1616279 z^2 - 5028765 z^3 - 270270 z^4)/(65536 z) - (105 (1 + 50 z - 2100 z^2 - 19840 z^3 + 19315 z^4 + 2574 z^5) Log[1 - Sqrt[z]])/(131072 z^(3/2)) + (105 (1 + 50 z - 2100 z^2 - 19840 z^3 + 19315 z^4 + 2574 z^5) Log[1 + Sqrt[z]])/(131072 z^(3/2)) + (33075 z^(3/2) (10 + 11 z) PolyLog[2, -Sqrt[z]])/16384 - (33075 z^(3/2) (10 + 11 z) PolyLog[2, Sqrt[z]])/16384

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]