Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1045)

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, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=1, b₁=4

http://functions.wolfram.com/07.25.03.1045.01

Input Form

HypergeometricPFQ[{-(11/2), 1}, {4, 5}, z] == (24 (16 - 68 z + 85 z^2))/(1105 z^3) + (1/(241158542625 z^3)) (128 E^(z/2) (-654729075 + 3101348250 z - 4647440520 z^2 + 3122658720 z^3 - 1081907280 z^4 + 206871840 z^5 - 22384320 z^6 + 1348608 z^7 - 41728 z^8 + 512 z^9) BesselI[0, z/2]) - (1/(241158542625 z^3)) (128 E^(z/2) (-34459425 + 1052110170 z - 2671512120 z^2 + 2293460640 z^3 - 904880880 z^4 + 186389280 z^5 - 21096768 z^6 + 1307648 z^7 - 41216 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]