Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0504)

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/07.22.03.0504.01

Input Form

HypergeometricPFQ[{-(11/2)}, {1/2, 1}, -z] == (1/19958400) (4 (2 (2494800 + 39309120 z + 64565235 z^2 + 19594920 z^3 + 1577792 z^4 + 38784 z^5 + 256 z^6) BesselJ[0, 2 Sqrt[z]] - Sqrt[z] (18743040 + 55985625 z + 18838800 z^2 + 1558624 z^3 + 38656 z^4 + 256 z^5) BesselJ[1, 2 Sqrt[z]]) + Pi z (108056025 + 240124500 z + 76839840 z^2 + 6272640 z^3 + 154880 z^4 + 1024 z^5) BesselJ[1, 2 Sqrt[z]] StruveH[0, 2 Sqrt[z]] - Pi z (108056025 + 240124500 z + 76839840 z^2 + 6272640 z^3 + 154880 z^4 + 1024 z^5) 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]