Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.4739)

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=-1/2, a₃>=-1/2

For fixed z and a₁=-7/2, a₂=-1/2, a₃=-1/2

For fixed z and a₁=-7/2, a₂=-1/2, a₃=-1/2, b₁=3

http://functions.wolfram.com/07.27.03.4739.01

Input Form

HypergeometricPFQ[{-(7/2), -(1/2), -(1/2)}, {3, 4}, z] == -((1/(2341213875 Pi^2 z^3)) (1024 (3960 + 1244374 z + 17460403 z^2 - 70714346 z^3 + 308450 z^4 - 9970 z^5 + 320 z^6) EllipticE[1/2 - Sqrt[1 - z]/2]^2)) - (1/(2341213875 Pi^2 z^3)) (1024 Sqrt[1 - z] (-3960 - 930049 z - 12195074 z^2 + 32197380 z^3 - 2435 z^4 + 80 z^5) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(2341213875 Pi^2 z^3)) (1024 (3960 + 1244374 z + 17460403 z^2 - 70714346 z^3 + 308450 z^4 - 9970 z^5 + 320 z^6) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(2341213875 Pi^2 z^3)) (512 Sqrt[1 - z] (-3960 - 930049 z - 12195074 z^2 + 32197380 z^3 - 2435 z^4 + 80 z^5) EllipticK[1/2 - Sqrt[1 - z]/2]^2) - (1/(2341213875 Pi^2 z^3)) (512 (3960 + 928069 z + 11808507 z^2 - 55286158 z^3 + 9909590 z^4 - 4995 z^5 + 160 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]