Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.a81q)

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=-5/2, a₃>=-5/2

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

For fixed z and a₁=-5/2, a₂=-5/2, a₃=1, b₁=7/2

http://functions.wolfram.com/07.27.03.a81q.01

Input Form

HypergeometricPFQ[{-(5/2), -(5/2), 1}, {7/2, 4}, z] == -((10 (8 + 484 z + 3267 z^2))/(53361 z^3)) + (1/(218566656 z^3)) (Sqrt[1 - z] (327680 + 17587235 z + 102229940 z^2 + 136983892 z^3 + 45732736 z^4 + 2678752 z^5)) + (5 (693 + 11550 z + 36960 z^2 + 31680 z^3 + 7040 z^4 + 256 z^5) ArcSin[Sqrt[z]])/(315392 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]