Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.7108)

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, a₃>=1

For fixed z and a₁=-7/2, a₂=1, a₃=5/2

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

http://functions.wolfram.com/07.27.03.7108.01

Input Form

HypergeometricPFQ[{-(7/2), 1, 5/2}, {2, 4}, z] == 4/(9 z) + (128 (-315 + 945 z - 5524 z^2 + 9473 z^3 - 8163 z^4 + 3584 z^5 - 640 z^6) EllipticE[z])/(405405 Pi z^3) + (64 (630 - 2205 z + 6323 z^2 - 10295 z^3 + 8571 z^4 - 3664 z^5 + 640 z^6) EllipticK[z])/(405405 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]