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

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=3/2, a₂>=3/2

For fixed z and a₁=3/2, a₂=9/2, b₁>=-11/2

For fixed z and a₁=3/2, a₂=9/2, b₁=-11/2

http://functions.wolfram.com/07.25.03.agun.01

Input Form

HypergeometricPFQ[{3/2, 9/2}, {-(11/2), 1}, z] == (1/1091475) (E^(z/2) (1091475 - 1885275 z + 1543500 z^2 - 1102500 z^3 + 882000 z^4 - 1002960 z^5 + 2970240 z^6 + 7381248 z^7 + 3420928 z^8 + 591104 z^9 + 41984 z^10 + 1024 z^11) BesselI[0, z/2]) + (1/1091475) (E^(z/2) (870975 z - 882000 z^2 + 661500 z^3 - 504000 z^4 + 478800 z^5 - 749952 z^6 + 4729088 z^7 + 2889728 z^8 + 550656 z^9 + 40960 z^10 + 1024 z^11) 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

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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]