Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.4544)

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=-9/2, a₂>=-9/2

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

For fixed z and a₁=-9/2, a₂=3, b₁=4

http://functions.wolfram.com/07.25.03.4544.01

Input Form

HypergeometricPFQ[{-(9/2), 3}, {4, 4}, z] == 96/(715 z^3) - (1/(483107625 z^3)) (8 E^(z/2) (8108100 - 4054050 z - 2071215 z^2 - 62815680 z^3 + 76386600 z^4 - 30273120 z^5 + 5054160 z^6 - 363264 z^7 + 9152 z^8) BesselI[0, z/2]) + (1/(483107625 z^2)) (8 E^(z/2) (-10311885 - 10046745 z - 19289880 z^2 + 52677000 z^3 - 25736400 z^4 + 4704624 z^5 - 354112 z^6 + 9152 z^7) 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]