Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ajo4)

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=11/2, b₁>=-11/2

For fixed z and a₁=5/2, a₂=11/2, b₁=-7/2

http://functions.wolfram.com/07.25.03.ajo4.01

Input Form

HypergeometricPFQ[{5/2, 11/2}, {-(7/2), 3}, z] == (1/297675) (8 E^(z/2) (56700 - 70875 z + 75600 z^2 - 104400 z^3 + 357120 z^4 + 997200 z^5 + 551040 z^6 + 112128 z^7 + 9216 z^8 + 256 z^9) BesselI[0, z/2]) + (1/(297675 z)) (4 E^(z/2) (-155925 + 28350 z + 47250 z^2 - 72000 z^3 + 91440 z^4 - 168480 z^5 + 1177440 z^6 + 903936 z^7 + 206592 z^8 + 17920 z^9 + 512 z^10) 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]