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

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=7/2, a₂>=7/2

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

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

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

Input Form

HypergeometricPFQ[{7/2, 11/2}, {-(5/2), 1}, z] == (1/212625) (E^(z/2) (212625 - 1743525 z + 8718300 z^2 - 76706460 z^3 - 470964240 z^4 - 672744240 z^5 - 403441920 z^6 - 119888640 z^7 - 18816768 z^8 - 1565952 z^9 - 64512 z^10 - 1024 z^11) BesselI[0, z/2]) + (1/212625) (E^(z/2) (380025 z - 2189160 z^2 + 10993860 z^3 - 156611520 z^4 - 403396560 z^5 - 307560960 z^6 - 103235328 z^7 - 17344512 z^8 - 1502976 z^9 - 63488 z^10 - 1024 z^11) BesselI[1, z/2])

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]
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HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
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