Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.as3l)

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=3/2, a₂>=3/2

For fixed z and a₁=3/2, a₂=5/2, a₃>=5/2

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

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

http://functions.wolfram.com/07.27.03.as3l.01

Input Form

HypergeometricPFQ[{3/2, 5/2, 5/2}, {-(7/2), 4}, z] == -((1/(105 Pi (-1 + z)^6 z^3)) (32 (120120 - 694155 z + 1658475 z^2 - 2089069 z^3 + 1452653 z^4 - 519768 z^5 + 70464 z^6) EllipticE[z])) - (1/(105 Pi (-1 + z)^5 z^3)) (32 (120120 - 634095 z + 1363950 z^2 - 1514719 z^3 + 898056 z^4 - 256992 z^5 + 23040 z^6) 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]