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

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=1, a₃>=1

For fixed z and a₁=-5/2, a₂=1, a₃=7/2

For fixed z and a₁=-5/2, a₂=1, a₃=7/2, b₁=4

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

Input Form

HypergeometricPFQ[{-(5/2), 1, 7/2}, {4, 4}, z] == (4 (64 - 176 z + 297 z^2))/(1155 z^3) + (1024 (-3254 + 8135 z - 11372 z^2 + 8923 z^3 - 3712 z^4 + 640 z^5) EllipticE[z])/(4002075 Pi z^3) - (512 (-3043 + 9129 z - 12281 z^2 + 9347 z^3 - 3792 z^4 + 640 z^5) EllipticK[z])/(4002075 Pi 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]