Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.2148)

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=2

http://functions.wolfram.com/07.27.03.2148.01

Input Form

HypergeometricPFQ[{-(7/2), -(7/2), 7/2}, {2, 4}, z] == (1/(6087156075 Pi^2 z^3)) (256 (-11760 - 125685 z + 23419046 z^2 + 1315977742 z^3 + 4148444106 z^4 + 2334163480 z^5 + 193435520 z^6) EllipticE[1/2 - Sqrt[1 - z]/2]^2) + (1/(6087156075 Pi^2 z^3)) (256 (11760 + 125685 z - 23419046 z^2 - 1315977742 z^3 - 4148444106 z^4 - 2334163480 z^5 - 193435520 z^6) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(6087156075 Pi^2 z^3)) (256 Sqrt[1 - z] (11760 + 128625 z - 17749256 z^2 - 659095236 z^3 - 1686293475 z^4 - 761730400 z^5 - 46126080 z^6) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(6087156075 Pi^2 z^3)) (128 Sqrt[1 - z] (-11760 - 128625 z + 17749256 z^2 + 659095236 z^3 + 1686293475 z^4 + 761730400 z^5 + 46126080 z^6) EllipticK[1/2 - Sqrt[1 - z]/2]^2) + (1/(6087156075 Pi^2 z^3)) (128 (-11760 - 122745 z + 17814671 z^2 + 841865978 z^3 + 2516337003 z^4 + 1360315960 z^5 + 108249280 z^6) EllipticK[1/2 - Sqrt[1 - z]/2]^2)

Standard Form

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MathML Form

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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]