Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.4725)

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=7/2, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=7/2, b₁=3/2

http://functions.wolfram.com/07.25.03.4725.01

Input Form

HypergeometricPFQ[{-(9/2), 7/2}, {3/2, 5}, z] == -((1/(57432375 z^2)) (32 E^(z/2) (-14175 - 945 z - 1787940 z^2 + 4630500 z^3 - 3384240 z^4 + 928560 z^5 - 100608 z^6 + 3584 z^7) BesselI[0, z/2])) + (1/(57432375 z^3)) (32 E^(z/2) (-56700 - 3780 z + 25515 z^2 - 143640 z^3 + 2365500 z^4 - 2595840 z^5 + 833328 z^6 - 97024 z^7 + 3584 z^8) 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]