Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.anw4)

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.anw4.01

Input Form

HypergeometricPFQ[{11/2, 6}, {1, 3}, z] == (1/226800) (E^(z/2) (226800 + 2381400 z + 5737815 z^2 + 5392170 z^3 + 2367000 z^4 + 522720 z^5 + 58800 z^6 + 3168 z^7 + 64 z^8) BesselI[0, z/2]) + (1/226800) (E^(z/2) z (494190 + 2713095 z + 3656070 z^2 + 1923480 z^3 + 468480 z^4 + 55728 z^5 + 3104 z^6 + 64 z^7) 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]