Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aj01)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=7/2, b₁>=-11/2

For fixed z and a₁=5/2, a₂=7/2, b₁=-11/2

http://functions.wolfram.com/07.25.03.aj01.01

Input Form

HypergeometricPFQ[{5/2, 7/2}, {-(11/2), -(11/2)}, z] == (1/4862521125) (E^z (4862521125 - 3456006750 z + 1571724000 z^2 - 285768000 z^3 + 400075200 z^4 + 1867017600 z^5 + 94951180800 z^6 + 4380556723200 z^7 + 20378941632000 z^8 + 30667880033280 z^9 + 20899356549120 z^10 + 7528390410240 z^11 + 1554052792320 z^12 + 191172280320 z^13 + 14115274752 z^14 + 607911936 z^15 + 13959168 z^16 + 131072 z^17))

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,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},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]