Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0492)

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=-1/2

http://functions.wolfram.com/07.22.03.0492.01

Input Form

HypergeometricPFQ[{-(11/2)}, {-(1/2), 4}, -z] == (1/(34459425 z^(5/2))) (-2 (2 Sqrt[z] (3274425 + 2338875 z - 4365900 z^2 + 13065120 z^3 + 67559040 z^4 + 18676902 z^5 + 1217720 z^6 + 23968 z^7 + 128 z^8) BesselJ[0, 2 Sqrt[z]] - (6548850 + 1403325 z + 5613300 z^2 - 8796960 z^3 + 59184000 z^4 + 18088434 z^5 + 1205848 z^6 + 23904 z^7 + 128 z^8) BesselJ[1, 2 Sqrt[z]]) - Pi z^(9/2) (126351225 + 36756720 z + 2423520 z^2 + 47872 z^3 + 256 z^4) BesselJ[1, 2 Sqrt[z]] StruveH[0, 2 Sqrt[z]] + Pi z^(9/2) (126351225 + 36756720 z + 2423520 z^2 + 47872 z^3 + 256 z^4) BesselJ[0, 2 Sqrt[z]] StruveH[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]