Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.au3j)

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=7/2

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

http://functions.wolfram.com/07.27.03.au3j.01

Input Form

HypergeometricPFQ[{5/2, 5/2, 7/2}, {-(7/2), 2}, z] == (1/(105 Pi (-1 + z)^10 z)) (4 (-21 + 311 z - 2266 z^2 + 11430 z^3 - 52225 z^4 + 469283 z^5 + 788656 z^6 + 160064 z^7 + 1024 z^8) EllipticE[z]) + (1/(105 Pi (-1 + z)^9 z)) (4 (-21 + 248 z - 1470 z^2 + 6300 z^3 - 26965 z^4 + 293748 z^5 + 363040 z^6 + 53248 z^7) EllipticK[z])

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]