Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.auj2)

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=7/2, a₃>=7/2

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

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

http://functions.wolfram.com/07.27.03.auj2.01

Input Form

HypergeometricPFQ[{5/2, 7/2, 7/2}, {-(3/2), 4}, z] == -((32 (504 - 3409 z + 9819 z^2 - 15563 z^3 + 14529 z^4 - 6984 z^5 + 4176 z^6) EllipticE[z])/(45 Pi (-1 + z)^7 z^3)) - (32 (504 - 3157 z + 8335 z^2 - 11943 z^3 + 9885 z^4 - 4008 z^5 + 1920 z^6) EllipticK[z])/(45 Pi (-1 + z)^6 z^3)

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]