Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.6905)

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=-7/2, a₂>=-7/2

For fixed z and a₁=-7/2, a₂=2, b₁>=-11/2

For fixed z and a₁=-7/2, a₂=2, b₁=4

http://functions.wolfram.com/07.25.03.6905.01

Input Form

HypergeometricPFQ[{-(7/2), 2}, {4, 4}, z] == (16 (-4 + 13 z))/(143 z^3) + (1/(19324305 z^3)) (16 E^(z/2) (540540 - 2027025 z + 681738 z^2 + 1384920 z^3 - 973152 z^4 + 218416 z^5 - 19360 z^6 + 576 z^7) BesselI[0, z/2]) - (1/(19324305 z^2)) (16 E^(z/2) (-921693 + 1125270 z + 685848 z^2 - 782048 z^3 + 199920 z^4 - 18784 z^5 + 576 z^6) 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]