Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1048)

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/07.25.03.1048.01

Input Form

HypergeometricPFQ[{-(11/2), 1}, {4, 6}, z] == (2 (96 - 272 z + 255 z^2))/(221 z^3) + (1/(1012865879025 z^3)) (512 E^(z/2) (-1722971250 + 5685805125 z - 6513726240 z^2 + 3517844400 z^3 - 1013876640 z^4 + 165468240 z^5 - 15590400 z^6 + 830976 z^7 - 23040 z^8 + 256 z^9) BesselI[0, z/2]) - (1/(1012865879025 z^4)) (256 E^(z/2) (-34459425 - 344594250 z + 4748241330 z^2 - 8246397600 z^3 + 5422702320 z^4 - 1738951200 z^5 + 302114400 z^6 - 29586432 z^7 + 1616640 z^8 - 45568 z^9 + 512 z^10) 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]