Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.abl2)

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=-3/2

http://functions.wolfram.com/07.27.03.abl2.01

Input Form

HypergeometricPFQ[{-(5/2), 1, 4}, {-(3/2), 3/2}, -z] == (1/(3072 (1 + z)^2)) (2272 - 4776 z + 45892 z^2 + 17325 Pi^2 z^(5/2) + 123200 z^3 + 34650 Pi^2 z^(7/2) + 69300 z^4 + 17325 Pi^2 z^(9/2)) + (1/(36864 (1 + z)^(15/2))) ((-36864 - 32000 z - 728960 z^2 - 11831760 z^3 - 53887280 z^4 - 128222654 z^5 - 182243715 z^6 - 161479200 z^7 - 87903225 z^8 - 27013950 z^9 - 3599340 z^10) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(36864 (1 + z)^(15/2))) ((36864 + 32000 z + 728960 z^2 + 11831760 z^3 + 53887280 z^4 + 128222654 z^5 + 182243715 z^6 + 161479200 z^7 + 87903225 z^8 + 27013950 z^9 + 3599340 z^10) Log[1 - Sqrt[z] + Sqrt[1 + z]]) + (5 (40 - 110 z + 495 z^2 + 5313 z^3 + 8085 z^4 + 3465 z^5) Log[Sqrt[z] + Sqrt[1 + z]])/(768 Sqrt[z] (1 + z)^(5/2)) + (1/(36864 (1 + z)^(15/2))) ((36864 + 32000 z + 728960 z^2 + 11831760 z^3 + 53887280 z^4 + 128222654 z^5 + 182243715 z^6 + 161479200 z^7 + 87903225 z^8 + 27013950 z^9 + 3599340 z^10) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])]) + (5775/256) z^(5/2) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])] + (5775/256) z^(5/2) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))] - (5775/256) z^(5/2) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])]

Standard Form

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MathML 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]