Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.3458)

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/07.27.03.3458.01

Input Form

HypergeometricPFQ[{-(7/2), -(5/2), 4}, {1/2, 5/2}, z] == (-105 + 251609 z + 5049611 z^2 + 5726385 z^3 + 180180 z^4)/(262144 z) + (105 (-1 - 100 z - 13380 z^2 - 14480 z^3 + 26245 z^4 + 1716 z^5) Log[1 - Sqrt[z]])/(524288 z^(3/2)) - (105 (-1 - 100 z - 13380 z^2 - 14480 z^3 + 26245 z^4 + 1716 z^5) Log[1 + Sqrt[z]])/(524288 z^(3/2)) - (11025 Sqrt[z] (10 + 60 z + 33 z^2) PolyLog[2, -Sqrt[z]])/65536 + (11025 Sqrt[z] (10 + 60 z + 33 z^2) PolyLog[2, Sqrt[z]])/65536

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]