Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2267)

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=-11/2, a₂>=-11/2

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

For fixed z and a₁=-11/2, a₂=9/2, b₁=-5/2

http://functions.wolfram.com/07.25.03.2267.01

Input Form

HypergeometricPFQ[{-(11/2), 9/2}, {-(5/2), 5}, z] == -((1/(1091215125 z^2)) (32 E^(z/2) (-13378365 + 9948015 z - 39708900 z^2 - 45904320 z^3 - 54677760 z^4 - 152844288 z^5 + 339714048 z^6 - 116654080 z^7 + 9437184 z^8) BesselI[0, z/2])) + (1/(1091215125 z^3)) (32 E^(z/2) (-53513460 + 39792060 z - 24106005 z^2 + 19501020 z^3 + 25446720 z^4 + 26404608 z^5 + 40200192 z^6 + 237215744 z^7 - 107216896 z^8 + 9437184 z^9) 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]