Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.6634)

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=-7/2, a₂>=-7/2

For fixed z and a₁=-7/2, a₂=1, a₃>=1

For fixed z and a₁=-7/2, a₂=1, a₃=1

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

http://functions.wolfram.com/07.27.03.6634.01

Input Form

HypergeometricPFQ[{-(7/2), 1, 1}, {-(5/2), 1/2}, z] == -((I (2880 I + 4704 I z + 9800 I z^2 + 44100 I z^3 + 11025 Pi^2 z^(7/2)))/ 2880) + (7 Sqrt[1 - z] (-8 Sqrt[z] - 14 z^(3/2) - 35 z^(5/2) + 105 z^(7/2)) ArcSin[Sqrt[z]])/(48 (-1 + z)) - (1/(245760 (-1 + z)^8)) (Sqrt[1 - z] (245760 - 829992 z + 911340 z^2 + 5977480 z^3 - 58963425 z^4 + 264119415 z^5 - 622148443 z^6 + 878667825 z^7 - 774237520 z^8 + 419270880 z^9 - 128217600 z^10 + 17006080 z^11) Log[1 - E^(I ArcSin[Sqrt[z]])]) + (1/(245760 (-1 + z)^8)) (Sqrt[1 - z] (245760 - 829992 z + 911340 z^2 + 5977480 z^3 - 58963425 z^4 + 264119415 z^5 - 622148443 z^6 + 878667825 z^7 - 774237520 z^8 + 419270880 z^9 - 128217600 z^10 + 17006080 z^11) Log[(1 - E^(I ArcSin[Sqrt[z]]))/ (1 + E^(I ArcSin[Sqrt[z]]))]) - (245/16) z^(7/2) ArcSin[Sqrt[z]] Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))] + (1/(245760 (-1 + z)^8)) (Sqrt[1 - z] (245760 - 829992 z + 911340 z^2 + 5977480 z^3 - 58963425 z^4 + 264119415 z^5 - 622148443 z^6 + 878667825 z^7 - 774237520 z^8 + 419270880 z^9 - 128217600 z^10 + 17006080 z^11) Log[1 + E^(I ArcSin[Sqrt[z]])]) - (245/16) I z^(7/2) PolyLog[2, -E^(I ArcSin[Sqrt[z]])] + (245/16) I z^(7/2) PolyLog[2, E^(I ArcSin[Sqrt[z]])]

Standard Form

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MathML Form

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type='integer'> 11 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 128217600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 419270880 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 774237520 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 878667825 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 622148443 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 264119415 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> 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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]