Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.0393)

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=-5/2, b₁>=-11/2

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

http://functions.wolfram.com/07.25.03.0393.01

Input Form

HypergeometricPFQ[{-(11/2), -(5/2)}, {-(9/2), 5}, z] == (1/(13749310575 z^2)) (32 E^(z/2) (7952175 + 15280650 z + 451288530 z^2 - 437754240 z^3 + 115834320 z^4 - 8954400 z^5 - 480 z^6 - 768 z^7 + 1024 z^8) BesselI[0, z/2]) - (1/(13749310575 z^3)) (64 E^(z/2) (15904350 + 30561300 z + 43742160 z^2 + 80259795 z^3 - 167665680 z^4 + 53442480 z^5 - 4476480 z^6 + 144 z^7 + 128 z^8 + 512 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]