Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2105)

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=4, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=4, b₁=1

http://functions.wolfram.com/07.25.03.2105.01

Input Form

HypergeometricPFQ[{-(11/2), 4}, {1, 5}, z] == (1/(218243025 z^2)) (4 E^(z/2) (-249480 + 124740 z + 54521775 z^2 - 267338610 z^3 + 324591000 z^4 - 148781472 z^5 + 29196336 z^6 - 2444000 z^7 + 70720 z^8) BesselI[0, z/2]) - (1/(218243025 z^3)) (4 E^(z/2) (-997920 + 498960 z - 187110 z^2 + 51975 z^3 - 95667870 z^4 + 212828952 z^5 - 123038976 z^6 + 26858416 z^7 - 2373280 z^8 + 70720 z^9) 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]