Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.av0o)

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=3, a₂>=3

For fixed z and a₁=3, a₂=7/2, a₃>=7/2

For fixed z and a₁=3, a₂=7/2, a₃=4

For fixed z and a₁=3, a₂=7/2, a₃=4, b₁=-5/2

http://functions.wolfram.com/07.27.03.av0o.01

Input Form

HypergeometricPFQ[{3, 7/2, 4}, {-(5/2), -(5/2)}, z] == (1/(3200 (-1 + z)^15)) (-3200 + 26496 z - 443520 z^2 - 88968320 z^3 - 22928922240 z^4 - 493790613120 z^5 - 2822827664384 z^6 - 5758687608960 z^7 - 4608483405240 z^8 - 1425260676840 z^9 - 149011580025 z^10 - 3568262082 z^11 - 2134440 z^12) - (9009 (33792 z^(7/2) + 2038784 z^(9/2) + 23482496 z^(11/2) + 88095488 z^(13/2) + 128854440 z^(15/2) + 77195976 z^(17/2) + 18165147 z^(19/2) + 1429428 z^(21/2) + 24024 z^(23/2)) ArcSin[Sqrt[z]])/ (640 Sqrt[1 - z] (-1 + 15 z - 105 z^2 + 455 z^3 - 1365 z^4 + 3003 z^5 - 5005 z^6 + 6435 z^7 - 6435 z^8 + 5005 z^9 - 3003 z^10 + 1365 z^11 - 455 z^12 + 105 z^13 - 15 z^14 + z^15))

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]