Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.a7qe)

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=-5/2, a₂>=-5/2

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

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

For fixed z and a₁=-5/2, a₂=-5/2, a₃=-5/2, b₁=3

http://functions.wolfram.com/07.27.03.a7qe.01

Input Form

HypergeometricPFQ[{-(5/2), -(5/2), -(5/2)}, {3, 4}, z] == (1/(58242197475 Pi^2 z^3)) (1024 (-4200 - 3048515 z - 120552115 z^2 + 2882595993 z^3 - 1864064029 z^4 + 61141903 z^5) EllipticE[1/2 - Sqrt[1 - z]/2]^2) - (1/(58242197475 Pi^2 z^3)) (1024 Sqrt[1 - z] (-4200 - 2350790 z - 89127675 z^2 + 1533373548 z^3 - 822020347 z^4 + 20806170 z^5) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) - (1/(58242197475 Pi^2 z^3)) (1024 (-4200 - 3048515 z - 120552115 z^2 + 2882595993 z^3 - 1864064029 z^4 + 61141903 z^5) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(58242197475 Pi^2 z^3)) (512 Sqrt[1 - z] (-4200 - 2350790 z - 89127675 z^2 + 1533373548 z^3 - 822020347 z^4 + 20806170 z^5) EllipticK[1/2 - Sqrt[1 - z]/2]^2) - (1/(58242197475 Pi^2 z^3)) (512 (4200 + 2348690 z + 88126580 z^2 - 2025144708 z^3 + 1899171976 z^4 - 283901144 z^5 + 4002075 z^6) EllipticK[1/2 - Sqrt[1 - z]/2]^2)

Standard Form

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MathML Form

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</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> <mo> ) </mo> </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'> 5 <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'> 5 <sep /> 2 </cn> </apply> </list> <list> <cn type='integer'> 3 </cn> <cn type='integer'> 4 </cn> </list> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 58242197475 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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]