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

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=-5/2, a₂>=-5/2

For fixed z and a₁=-5/2, a₂=1, a₃>=1

For fixed z and a₁=-5/2, a₂=1, a₃=4

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

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

Input Form

HypergeometricPFQ[{-(5/2), 1, 4}, {-(1/2), 5/2}, -z] == -((3 (-320 - 3808 z + 35000 z^2 + 12600 Pi^2 z^(5/2) + 69300 z^3 + 17325 Pi^2 z^(7/2)))/(16384 z)) + (1/(32768 (1 + z)^(15/2))) ((-512 + 229632 z + 1366720 z^2 + 8462600 z^3 + 24208644 z^4 + 42785974 z^5 + 49141279 z^6 + 36986775 z^7 + 17673075 z^8 + 4878435 z^9 + 593850 z^10) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(32768 (1 + z)^(15/2))) ((512 - 229632 z - 1366720 z^2 - 8462600 z^3 - 24208644 z^4 - 42785974 z^5 - 49141279 z^6 - 36986775 z^7 - 17673075 z^8 - 4878435 z^9 - 593850 z^10) Log[1 - Sqrt[z] + Sqrt[1 + z]]) - (15 (16 - 72 z + 378 z^2 + 3675 z^3 + 3465 z^4) Log[Sqrt[z] + Sqrt[1 + z]])/ (4096 z^(3/2) Sqrt[1 + z]) + (1/(32768 (1 + z)^(15/2))) ((512 - 229632 z - 1366720 z^2 - 8462600 z^3 - 24208644 z^4 - 42785974 z^5 - 49141279 z^6 - 36986775 z^7 - 17673075 z^8 - 4878435 z^9 - 593850 z^10) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/ (1 + Sqrt[z] + Sqrt[1 + z])]) - (4725 z^(3/2) (8 + 11 z) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/4096 - (4725 z^(3/2) (8 + 11 z) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))])/4096 + (4725 z^(3/2) (8 + 11 z) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])])/4096

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]