Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.al92)

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=9/2, b₁>=-11/2

For fixed z and a₁=7/2, a₂=9/2, b₁=-11/2

http://functions.wolfram.com/07.25.03.al92.01

Input Form

HypergeometricPFQ[{7/2, 9/2}, {-(11/2), 2}, z] == (1/16372125) (E^(z/2) (16372125 - 30107700 z + 30069900 z^2 - 25893000 z^3 + 24343200 z^4 - 31852800 z^5 + 107170560 z^6 + 302400000 z^7 + 175622400 z^8 + 41088000 z^9 + 4469760 z^10 + 223232 z^11 + 4096 z^12) BesselI[0, z/2]) + (1/16372125) (E^(z/2) (-6081075 + 16650900 z - 17936100 z^2 + 15309000 z^3 - 13356000 z^4 + 14434560 z^5 - 25401600 z^6 + 176647680 z^7 + 140601600 z^8 + 36940800 z^9 + 4252672 z^10 + 219136 z^11 + 4096 z^12) 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]
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]