Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ag8k)

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=5/2, b₁>=-11/2

For fixed z and a₁=3/2, a₂=5/2, b₁=-11/2

http://functions.wolfram.com/07.25.03.ag8k.01

Input Form

HypergeometricPFQ[{3/2, 5/2}, {-(11/2), 5}, z] == (1/(10395 z^2)) (32 E^(z/2) (-43648605 + 16081065 z - 4074840 z^2 + 758520 z^3 - 109392 z^4 + 12432 z^5 - 1088 z^6 + 64 z^7) BesselI[0, z/2]) + (1/(10395 z^3)) (32 E^(z/2) (174594420 - 64324260 z + 21756735 z^2 - 5045040 z^3 + 890328 z^4 - 123648 z^5 + 13616 z^6 - 1152 z^7 + 64 z^8) 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]