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

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=3, a₃>=3

For fixed z and a₁=5/2, a₂=3, a₃=4

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

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

Input Form

HypergeometricPFQ[{5/2, 3, 4}, {-(7/2), -(3/2)}, -z] == (1/(896 (1 + z)^14)) (896 + 7424 z + 153216 z^2 + 10468864 z^3 + 794824576 z^4 - 24347062656 z^5 + 130302763136 z^6 - 217648006576 z^7 + 127820371536 z^8 - 24945276741 z^9 + 1206399810 z^10 - 2522520 z^11) - (6435 (91520 z^(9/2) - 1148160 z^(11/2) + 3816720 z^(13/2) - 4449808 z^(15/2) + 1910799 z^(17/2) - 274428 z^(19/2) + 9240 z^(21/2)) ArcSinh[Sqrt[z]])/(128 Sqrt[1 + z] (1 + 14 z + 91 z^2 + 364 z^3 + 1001 z^4 + 2002 z^5 + 3003 z^6 + 3432 z^7 + 3003 z^8 + 2002 z^9 + 1001 z^10 + 364 z^11 + 91 z^12 + 14 z^13 + z^14))

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]