Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0549)

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=-11/2, b_1`>=-11/2

For fixed z and a₁=-11/2, b₁=3/2

http://functions.wolfram.com/07.22.03.0549.01

Input Form

HypergeometricPFQ[{-(11/2)}, {3/2, 2}, z] == (1/(6227020800 Sqrt[z])) (4 (2 Sqrt[z] (838252800 - 3232489815 z + 1941922260 z^2 - 288762336 z^3 + 13645440 z^4 - 219904 z^5 + 1024 z^6) BesselI[0, 2 Sqrt[z]] + (-119750400 + 2462540805 z - 1808536500 z^2 + 282127392 z^3 - 13536384 z^4 + 219392 z^5 - 1024 z^6) BesselI[1, 2 Sqrt[z]]) + Pi Sqrt[z] (-1404728325 + 11237826600 z - 7491884400 z^2 + 1141620480 z^3 - 54362880 z^4 + 878592 z^5 - 4096 z^6) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi Sqrt[z] (1404728325 - 11237826600 z + 7491884400 z^2 - 1141620480 z^3 + 54362880 z^4 - 878592 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]