Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.av5h)

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=7/2, a₃>=7/2

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

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

http://functions.wolfram.com/07.27.03.av5h.01

Input Form

HypergeometricPFQ[{7/2, 7/2, 7/2}, {-(7/2), 1}, z] == (1/(525 Pi (-1 + z)^13)) (2 (-1535 + 35750 z - 470977 z^2 + 5569832 z^3 - 136477297 z^4 - 918984610 z^5 - 1281912175 z^6 - 517814860 z^7 - 55658560 z^8 - 938240 z^9) EllipticE[z]) + (1/(525 Pi (-1 + z)^12)) (4 (-505 + 11060 z - 140101 z^2 + 1671128 z^3 - 47201395 z^4 - 259735780 z^5 - 307916815 z^6 - 104257960 z^7 - 8985280 z^8 - 107520 z^9) 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]