Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.anw0)

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=6, b₁>=-11/2

For fixed z and a₁=11/2, a₂=6, b₁=1

http://functions.wolfram.com/07.25.03.anw0.01

Input Form

HypergeometricPFQ[{11/2, 6}, {1, 1}, z] == (1/907200) (E^(z/2) (907200 + 29484000 z + 154693710 z^2 + 283456575 z^3 + 237297240 z^4 + 102519000 z^5 + 24284400 z^6 + 3224112 z^7 + 235840 z^8 + 8768 z^9 + 128 z^10) BesselI[0, z/2]) + (1/907200) (E^(z/2) (2657160 z + 46667700 z^2 + 147064545 z^3 + 163168200 z^4 + 82428840 z^5 + 21388752 z^6 + 3001040 z^7 + 227264 z^8 + 8640 z^9 + 128 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]