Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.1118)

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=-5/2

For fixed z and a₁=-7/2, a₂=-7/2, a₃=-5/2, b₁=4

http://functions.wolfram.com/07.27.03.1118.01

Input Form

HypergeometricPFQ[{-(7/2), -(7/2), -(5/2)}, {4, 4}, z] == -((1/(9575096505975 Pi^2 z^3)) (2048 (3026110 + 282445585 z + 8929586920 z^2 - 251637151954 z^3 + 264868363052 z^4 - 24656435044 z^5 + 41520930 z^6) EllipticE[1/2 - Sqrt[1 - z]/2]^2)) + (1/(9575096505975 Pi^2 z^3)) (2048 Sqrt[1 - z] (2425510 + 213119600 z + 6590849820 z^2 - 136399948714 z^3 + 122706554176 z^4 - 9436144080 z^5 + 7432425 z^6) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(9575096505975 Pi^2 z^3)) (2048 (3026110 + 282445585 z + 8929586920 z^2 - 251637151954 z^3 + 264868363052 z^4 - 24656435044 z^5 + 41520930 z^6) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) - (1/(9575096505975 Pi^2 z^3)) (1024 Sqrt[1 - z] (2425510 + 213119600 z + 6590849820 z^2 - 136399948714 z^3 + 122706554176 z^4 - 9436144080 z^5 + 7432425 z^6) EllipticK[1/2 - Sqrt[1 - z]/2]^2) - (1/(9575096505975 Pi^2 z^3)) (1024 (2425510 + 212056995 z + 6501569180 z^2 - 176517384034 z^3 + 238247465598 z^4 - 56519824652 z^5 + 2220758265 z^6) EllipticK[1/2 - Sqrt[1 - z]/2]^2)

Standard Form

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MathML Form

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</mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 56519824652 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 238247465598 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 176517384034 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 6501569180 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 212056995 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 2425510 </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> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq 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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]