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

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=11/2, b₁>=-11/2

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

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

Input Form

HypergeometricPFQ[{11/2, 11/2}, {1/2, 1}, z] == (1/893025) (E^(z/2) (893025 + 53581500 z + 352691010 z^2 + 740955600 z^3 + 685193040 z^4 + 320302080 z^5 + 80978400 z^6 + 11361408 z^7 + 871680 z^8 + 33792 z^9 + 512 z^10) BesselI[0, z/2]) + (1/893025) (2 E^(z/2) (1596105 z + 46649925 z^2 + 181447560 z^3 + 229143600 z^4 + 127001520 z^5 + 35413584 z^6 + 5269440 z^7 + 419328 z^8 + 16640 z^9 + 256 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]