Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.all1)

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=11/2, b₁>=-11/2

For fixed z and a₁=7/2, a₂=11/2, b₁=-9/2

http://functions.wolfram.com/07.25.03.all1.01

Input Form

HypergeometricPFQ[{7/2, 11/2}, {-(9/2), 4}, z] == -((1/(4465125 z)) (4 E^(z/2) (-6081075 + 1417500 z + 850500 z^2 - 1247400 z^3 + 1234800 z^4 - 1532160 z^5 + 4757760 z^6 + 12249600 z^7 + 6001920 z^8 + 1090560 z^9 + 80896 z^10 + 2048 z^11) BesselI[0, z/2])) - (1/(4465125 z^2)) (4 E^(z/2) (24324300 - 10135125 z + 4365900 z^2 - 1984500 z^3 + 1071000 z^4 - 750960 z^5 + 725760 z^6 - 1178880 z^7 + 7656960 z^8 + 5026560 z^9 + 1012736 z^10 + 78848 z^11 + 2048 z^12) 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]