Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.0646)

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=-1/2, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=-1/2, b₁=-7/2

http://functions.wolfram.com/07.25.03.0646.01

Input Form

HypergeometricPFQ[{-(11/2), -(1/2)}, {-(7/2), 5}, z] == -((1/(7638505875 z^2)) (32 E^(z/2) (-22297275 - 31216185 z - 269479980 z^2 + 120207780 z^3 + 68880 z^4 + 43440 z^5 + 76416 z^6 - 113152 z^7 + 8192 z^8) BesselI[0, z/2])) + (1/(7638505875 z^3)) (32 E^(z/2) (-89189100 - 124864740 z - 125893845 z^2 - 150519600 z^3 + 119901180 z^4 - 48000 z^5 - 25296 z^6 - 24448 z^7 - 104960 z^8 + 8192 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]