Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.1488)

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=-7/2, a₃>=-7/2

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

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

http://functions.wolfram.com/07.27.03.1488.01

Input Form

HypergeometricPFQ[{-(7/2), -(7/2), 1}, {1/2, 7/2}, z] == (-735 + 12985 z + 1018536 z^2 + 4823952 z^3 + 3075975 z^4 + 277095 z^5)/ (1179648 z^2) + (245 (-1 + 18 z - 225 z^2 - 2200 z^3 + 225 z^4 + 1926 z^5 + 257 z^6) Log[1 - Sqrt[z]])/(786432 z^(5/2)) - (245 (-1 + 18 z - 225 z^2 - 2200 z^3 + 225 z^4 + 1926 z^5 + 257 z^6) Log[1 + Sqrt[z]])/(786432 z^(5/2)) - (1225 Sqrt[z] (20 + 45 z + 18 z^2 + z^3) PolyLog[2, -Sqrt[z]])/32768 + (1225 Sqrt[z] (20 + 45 z + 18 z^2 + z^3) PolyLog[2, Sqrt[z]])/32768

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]