Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2758)

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=11/2, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=11/2, b₁=3

http://functions.wolfram.com/07.25.03.2758.01

Input Form

HypergeometricPFQ[{-(11/2), 11/2}, {3, 7/2}, z] == (1/2837835) (4 E^(z/2) (710325 - 2383920 z + 2474388 z^2 - 1061568 z^3 + 204624 z^4 - 17280 z^5 + 512 z^6) BesselI[0, z/2]) - (1/(2837835 z)) (4 E^(z/2) (3465 + 58905 z - 1010268 z^2 + 1671948 z^3 - 881328 z^4 + 188112 z^5 - 16768 z^6 + 512 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]