Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.av5d)

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.av5d.01

Input Form

HypergeometricPFQ[{7/2, 7/2, 7/2}, {-(7/2), -(5/2)}, z] == (1/(25 (1 - z)^(7/2) (-1 + z)^13)) (-25 + 290 z - 2664 z^2 - 85712 z^3 + 31873600 z^4 + 2888265600 z^5 + 40634035200 z^6 + 183694325760 z^7 + 330027540480 z^8 + 252948889600 z^9 + 81785651200 z^10 + 10133176320 z^11 + 376438784 z^12 + 2097152 z^13)

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]