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

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=3, a₃>=3

For fixed z and a₁=3, a₂=3, a₃=7/2

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

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

Input Form

HypergeometricPFQ[{3, 3, 7/2}, {-(7/2), -(7/2)}, -z] == (1/(11200 (1 + z)^16)) (11200 + 150400 z + 1049088 z^2 + 2091008 z^3 + 760828160 z^4 - 206947760640 z^5 + 4871077634560 z^6 - 30888067927808 z^7 + 71370585741312 z^8 - 66710898231120 z^9 + 25317741735000 z^10 - 3557809196370 z^11 + 142887931329 z^12 - 720451446 z^13) + (1287 (-292864 z^(9/2) + 19129344 z^(11/2) - 241353984 z^(13/2) + 1007586944 z^(15/2) - 1676538864 z^(17/2) + 1180611432 z^(19/2) - 344366022 z^(21/2) + 37118367 z^(23/2) - 1101672 z^(25/2) + 3432 z^(27/2)) ArcSinh[Sqrt[z]])/ (320 Sqrt[1 + z] (1 + 16 z + 120 z^2 + 560 z^3 + 1820 z^4 + 4368 z^5 + 8008 z^6 + 11440 z^7 + 12870 z^8 + 11440 z^9 + 8008 z^10 + 4368 z^11 + 1820 z^12 + 560 z^13 + 120 z^14 + 16 z^15 + z^16))

Standard Form

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MathML Form

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</cn> <ci> z </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]