Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.a84y)

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=3/2

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

http://functions.wolfram.com/07.27.03.a84y.01

Input Form

HypergeometricPFQ[{-(5/2), -(5/2), 3/2}, {3, 4}, z] == (1/(252130725 Pi^2 z^3)) (1024 (4200 + 681755 z + 2077990 z^2 + 7689504 z^3 + 3503173 z^4 + 237404 z^5) EllipticE[1/2 - Sqrt[1 - z]/2]^ 2) - (1/(252130725 Pi^2 z^3)) (1024 Sqrt[1 - z] (4200 + 492230 z + 1189110 z^2 + 3050814 z^3 + 1111819 z^4 + 55440 z^5) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) - (1/(252130725 Pi^2 z^3)) (1024 (4200 + 681755 z + 2077990 z^2 + 7689504 z^3 + 3503173 z^4 + 237404 z^5) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(252130725 Pi^2 z^3)) (512 Sqrt[1 - z] (4200 + 492230 z + 1189110 z^2 + 3050814 z^3 + 1111819 z^4 + 55440 z^5) EllipticK[1/2 - Sqrt[1 - z]/2]^2) + (1/(252130725 Pi^2 z^3)) (512 (4200 + 490130 z + 990245 z^2 + 4640214 z^3 + 2033062 z^4 + 132562 z^5) EllipticK[1/2 - Sqrt[1 - z]/2]^2)

Standard Form

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MathML Form

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<mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 55440 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1111819 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3050814 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1189110 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 492230 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 4200 </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> <mo> + </mo> <mfrac> <mrow> <mn> 512 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> 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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]