Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0933)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-9/2, b_1`>=-11/2

For fixed z and a₁=-9/2, b₁=5/2

http://functions.wolfram.com/07.22.03.0933.01

Input Form

HypergeometricPFQ[{-(9/2)}, {5/2, 4}, z] == (1/(5189184000 z^(5/2))) (4 (2 Sqrt[z] (-10886400 + 76204800 z + 1006439175 z^2 - 1146575700 z^3 + 219126240 z^4 - 11845248 z^5 + 207616 z^6 - 1024 z^7) BesselI[0, 2 Sqrt[z]] + (21772800 - 141523200 z - 580763925 z^2 + 1046488500 z^3 - 213380640 z^4 + 11742336 z^5 - 207104 z^6 + 1024 z^7) BesselI[1, 2 Sqrt[z]]) + Pi z^(3/2) (-638512875 - 3064861800 z + 4378374000 z^2 - 864864000 z^3 + 47174400 z^4 - 829440 z^5 + 4096 z^6) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi z^(3/2) (638512875 + 3064861800 z - 4378374000 z^2 + 864864000 z^3 - 47174400 z^4 + 829440 z^5 - 4096 z^6) BesselI[0, 2 Sqrt[z]] StruveL[1, 2 Sqrt[z]])

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,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},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]