Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.3553)

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=-3/2, a₃>=-3/2

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

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

http://functions.wolfram.com/07.27.03.3553.01

Input Form

HypergeometricPFQ[{-(7/2), -(3/2), -(3/2)}, {-(5/2), 4}, z] == (32 (88 - 1031 z + 7632 z^2 + 81766 z^3 + 32332 z^4 + 9 z^5 + 36 z^6) EllipticE[z])/(675675 Pi z^3) - (32 (88 - 1075 z + 8142 z^2 + 35782 z^3 - 31696 z^4 - 11259 z^5 + 18 z^6) EllipticK[z])/(675675 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]