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

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=3/2, a₂>=3/2

For fixed z and a₁=3/2, a₂=9/2, b₁>=-11/2

For fixed z and a₁=3/2, a₂=9/2, b₁=-11/2

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

Input Form

HypergeometricPFQ[{3/2, 9/2}, {-(11/2), -(11/2)}, z] == (1/11345882625) (E^z (11345882625 - 8814156750 z + 4000752000 z^2 - 952560000 z^3 + 666792000 z^4 + 2400451200 z^5 + 120200371200 z^6 + 5408305459200 z^7 + 24561061056000 z^8 + 36111083904000 z^9 + 24060705177600 z^10 + 8480024985600 z^11 + 1713791385600 z^12 + 206524416000 z^13 + 14946140160 z^14 + 631242752 z^15 + 14221312 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]