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

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=-3/2, a₂>=-3/2

For fixed z and a₁=-3/2, a₂=2, a₃>=2

For fixed z and a₁=-3/2, a₂=2, a₃=4

For fixed z and a₁=-3/2, a₂=2, a₃=4, b₁=-1/2

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

Input Form

HypergeometricPFQ[{-(3/2), 2, 4}, {-(1/2), 7/2}, z] == (15 (-192 + 32 z - 728 z^2 - 4900 z^3 + 1575 I Pi^2 z^(7/2) + 6300 z^4 - 1575 I Pi^2 z^(9/2)))/(16384 (-1 + z) z^2) + (15 Sqrt[1 - z] (-48 + 40 z + 90 z^2 + 315 z^3 - 2100 z^4 + 1575 z^5) ArcSin[Sqrt[z]])/(4096 (-1 + z)^2 z^(5/2)) - (1/(32768 (-1 + z)^9)) (Sqrt[1 - z] (-161792 + 2945024 z + 18760248 z^2 - 3478120 z^3 + 30125200 z^4 - 51254328 z^5 + 56726931 z^6 - 41123463 z^7 + 18937575 z^8 - 5043225 z^9 + 592950 z^10) Log[1 - E^(I ArcSin[Sqrt[z]])]) + (1/(32768 (-1 + z)^9)) (Sqrt[1 - z] (-161792 + 2945024 z + 18760248 z^2 - 3478120 z^3 + 30125200 z^4 - 51254328 z^5 + 56726931 z^6 - 41123463 z^7 + 18937575 z^8 - 5043225 z^9 + 592950 z^10) Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))]) - (23625 z^(3/2) ArcSin[Sqrt[z]] Log[(1 - E^(I ArcSin[Sqrt[z]]))/ (1 + E^(I ArcSin[Sqrt[z]]))])/4096 + (1/(32768 (-1 + z)^9)) (Sqrt[1 - z] (-161792 + 2945024 z + 18760248 z^2 - 3478120 z^3 + 30125200 z^4 - 51254328 z^5 + 56726931 z^6 - 41123463 z^7 + 18937575 z^8 - 5043225 z^9 + 592950 z^10) Log[1 + E^(I ArcSin[Sqrt[z]])]) - (23625 I z^(3/2) PolyLog[2, -E^(I ArcSin[Sqrt[z]])])/4096 + (23625 I z^(3/2) PolyLog[2, E^(I ArcSin[Sqrt[z]])])/4096

Standard Form

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MathML Form

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<times /> <imaginaryi /> <apply> <arcsin /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 15 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1575 </cn> <imaginaryi /> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 6300 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1575 </cn> <imaginaryi /> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4900 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> 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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]