Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.2442)

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=-3/2

For fixed z and a₁=-7/2, a₂=-5/2, a₃=-3/2, b₁=2

http://functions.wolfram.com/07.27.03.2442.01

Input Form

HypergeometricPFQ[{-(7/2), -(5/2), -(3/2)}, {2, 4}, z] == (1/(468242775 Pi^2 z^3)) (256 (80 - 6425 z - 2368116 z^2 + 100751797 z^3 - 75989638 z^4 + 930069 z^5 + 990 z^6) EllipticE[1/2 - Sqrt[1 - z]/2]^2) + (1/(468242775 Pi^2 z^3)) (256 Sqrt[1 - z] (-80 + 6405 z + 1812276 z^2 - 54693088 z^3 + 33337251 z^4 - 202455 z^5) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(468242775 Pi^2 z^3)) (256 (-80 + 6425 z + 2368116 z^2 - 100751797 z^3 + 75989638 z^4 - 930069 z^5 - 990 z^6) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(468242775 Pi^2 z^3)) (128 Sqrt[1 - z] (80 - 6405 z - 1812276 z^2 + 54693088 z^3 - 33337251 z^4 + 202455 z^5) EllipticK[1/2 - Sqrt[1 - z]/2]^2) + (1/(468242775 Pi^2 z^3)) (128 (80 - 6445 z - 1809081 z^2 + 70093051 z^3 - 74969771 z^4 + 10270737 z^5 + 495 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]