Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.1026)

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=-7/2, a₃>=-7/2

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

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

http://functions.wolfram.com/07.27.03.1026.01

Input Form

HypergeometricPFQ[{-(7/2), -(7/2), -(7/2)}, {1/2, 5/2}, z] == (245 Sqrt[-z] (175 Pi^2 - 1050 Pi^2 z + 420 Pi^2 z^2 - 8 Pi^2 z^3))/131072 - (Sqrt[1 - z] (-15435 - 121980660 z + 3267748524 z^2 - 3431613568 z^3 + 178650784 z^4))/(125829120 z) - (1/(8388608 (-z)^(3/2))) (7 (-147 + 36750 z - 4704000 z^2 - 14112000 z^3 + 20603520 z^4 - 803072 z^5) Log[Sqrt[1 - z] + Sqrt[-z]]) - (735 Sqrt[-z] (175 - 1050 z + 420 z^2 - 8 z^3) Log[Sqrt[1 - z] + Sqrt[-z]]^ 2)/65536 + (735 Sqrt[-z] (175 - 1050 z + 420 z^2 - 8 z^3) Log[Sqrt[1 - z] + Sqrt[-z]] Log[1 + Sqrt[1 - z] + Sqrt[-z]])/32768 + (735 Sqrt[-z] (175 - 1050 z + 420 z^2 - 8 z^3) PolyLog[2, -Sqrt[1 - z] - Sqrt[-z]])/32768 - (735 Sqrt[-z] (175 - 1050 z + 420 z^2 - 8 z^3) PolyLog[2, 1 - Sqrt[1 - z] - Sqrt[-z]])/32768

Standard Form

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MathML Form

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<annotation-xml encoding='MathML-Content'> <ci> PolyLog </ci> </annotation-xml> </semantics> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> </mrow> <mo> - </mo> <msqrt> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 32768 </mn> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 7 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 7 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </list> <list> <cn type='rational'> 1 <sep /> 2 </cn> <cn type='rational'> 5 <sep /> 2 </cn> </list> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> 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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]