Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0908)

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=3/2

http://functions.wolfram.com/07.22.03.0908.01

Input Form

HypergeometricPFQ[{-(9/2)}, {3/2, 6}, -z] == (1/(1309458150 z^(9/2))) (4 (2 Sqrt[z] (71442000 + 12757500 z + 9185400 z^2 + 12700800 z^3 + 228614400 z^4 + 312292305 z^5 + 61850880 z^6 + 3269472 z^7 + 54784 z^8 + 256 z^9) BesselJ[0, 2 Sqrt[z]] - (142884000 - 45927000 z - 6293700 z^2 + 11113200 z^3 + 114307200 z^4 + 283992435 z^5 + 60262920 z^6 + 3242304 z^7 + 54656 z^8 + 256 z^9) BesselJ[1, 2 Sqrt[z]]) + Pi z^(9/2) (654729075 + 1190416500 z + 244188000 z^2 + 13023360 z^3 + 218880 z^4 + 1024 z^5) BesselJ[1, 2 Sqrt[z]] StruveH[0, 2 Sqrt[z]] - Pi z^(9/2) (654729075 + 1190416500 z + 244188000 z^2 + 13023360 z^3 + 218880 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]