Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.8064)

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=3/2, a₃>=3/2

For fixed z and a₁=-7/2, a₂=3/2, a₃=4

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

http://functions.wolfram.com/07.27.03.8064.01

Input Form

HypergeometricPFQ[{-(7/2), 3/2, 4}, {7/2, 7/2}, z] == (10045 - 34755 z + 177941 z^2 - 233121 z^3 + 135520 z^4 - 30030 z^5)/ (262144 z^2) - (35 (-167 + 342 z + 2250 z^2 - 7000 z^3 + 7875 z^4 - 4158 z^5 + 858 z^6) Log[1 - Sqrt[z]])/(524288 z^(5/2)) + (35 (-167 + 342 z + 2250 z^2 - 7000 z^3 + 7875 z^4 - 4158 z^5 + 858 z^6) Log[1 + Sqrt[z]])/(524288 z^(5/2)) - (525 (-1 + 6 z) PolyLog[2, -Sqrt[z]])/(65536 z^(5/2)) + (525 (-1 + 6 z) PolyLog[2, Sqrt[z]])/(65536 z^(5/2))

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]