Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2947)

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=4

http://functions.wolfram.com/07.25.03.2947.01

Input Form

HypergeometricPFQ[{-(11/2), 6}, {4, 4}, z] == (1/(114864750 z)) (E^(z/2) (41580 + 115374105 z - 290623410 z^2 + 238905960 z^3 - 83886240 z^4 + 13587792 z^5 - 985568 z^6 + 25536 z^7) BesselI[0, z/2]) + (1/(114864750 z^2)) (E^(z/2) (-166320 - 2037420 z - 14875245 z^2 + 143855310 z^3 - 172645800 z^4 + 71700192 z^5 - 12640528 z^6 + 960032 z^7 - 25536 z^8) 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]