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

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=7/2, b₁>=-11/2

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

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

Input Form

HypergeometricPFQ[{7/2, 7/2}, {-(7/2), 6}, z] == (1/(1575 z^3)) (32 E^(z/2) (91891800 - 39864825 z + 11351340 z^2 - 2416680 z^3 + 411600 z^4 - 58320 z^5 + 7040 z^6 - 704 z^7 + 128 z^8) BesselI[0, z/2]) + (1/(1575 z^4)) (32 E^(z/2) (-367567200 + 159459300 z - 56891835 z^2 + 14650020 z^3 - 2945880 z^4 + 483600 z^5 - 66800 z^6 + 7936 z^7 - 832 z^8 + 128 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]