Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0532)

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

http://functions.wolfram.com/07.22.03.0532.01

Input Form

HypergeometricPFQ[{-(11/2)}, {1, 5/2}, -z] == (1/(17882726400 z)) (4 (2 z (2271359475 + 10587981600 z + 6983130672 z^2 + 1088770560 z^3 + 52906240 z^4 + 868352 z^5 + 4096 z^6) BesselJ[0, 2 Sqrt[z]] - Sqrt[z] (108056025 + 7849490040 z + 6481311984 z^2 + 1063058688 z^3 + 52475648 z^4 + 866304 z^5 + 4096 z^6) BesselJ[1, 2 Sqrt[z]]) + Pi (108056025 + 3025568700 z + 36306824400 z^2 + 26893944000 z^3 + 4303031040 z^4 + 210760704 z^5 + 3469312 z^6 + 16384 z^7) BesselJ[1, 2 Sqrt[z]] StruveH[0, 2 Sqrt[z]] - Pi (108056025 + 3025568700 z + 36306824400 z^2 + 26893944000 z^3 + 4303031040 z^4 + 210760704 z^5 + 3469312 z^6 + 16384 z^7) 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]