Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.2533)

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=-5/2, a₃>=-5/2

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

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

http://functions.wolfram.com/07.27.03.2533.01

Input Form

HypergeometricPFQ[{-(7/2), -(5/2), -(1/2)}, {1, 4}, z] == (1/(156080925 Pi^2 z^3)) (128 (-320 + 9970 z - 308450 z^2 + 70714346 z^3 - 17460403 z^4 - 1244374 z^5 - 3960 z^6) EllipticE[1/2 - Sqrt[1 - z]/2]^ 2) + (1/(156080925 Pi^2 z^3)) (128 Sqrt[1 - z] (320 - 9890 z + 306015 z^2 - 38516966 z^3 + 5265329 z^4 + 314325 z^5) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(156080925 Pi^2 z^3)) (128 (320 - 9970 z + 308450 z^2 - 70714346 z^3 + 17460403 z^4 + 1244374 z^5 + 3960 z^6) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(156080925 Pi^2 z^3)) (64 Sqrt[1 - z] (-320 + 9890 z - 306015 z^2 + 38516966 z^3 - 5265329 z^4 - 314325 z^5) EllipticK[1/2 - Sqrt[1 - z]/2]^2) + (1/(156080925 Pi^2 z^3)) (64 (-320 + 10050 z - 310930 z^2 + 48424121 z^3 - 28354107 z^4 - 700892 z^5 - 1980 z^6) EllipticK[1/2 - Sqrt[1 - z]/2]^2)

Standard Form

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MathML Form

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</mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 10050 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 320 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> - </mo> <mfrac> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </mrow> </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'> 5 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </list> <list> <cn type='integer'> 1 </cn> <cn type='integer'> 4 </cn> </list> <ci> z </ci> </apply> <apply> <plus /> <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]