Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0415)

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=-7/2

http://functions.wolfram.com/07.22.03.0415.01

Input Form

HypergeometricPFQ[{-(11/2)}, {-(7/2), 6}, z] == (1/(96245174025 z^(9/2))) (8 ((-BesselI[1, 2 Sqrt[z]]) (-8596937349000 - 5942000814750 z - 54784404675 z^2 - 13398947100 z^3 - 785862000 z^4 - 52920000 z^5 - 5241600 z^6 - 949248 z^7 - 454656 z^8 - 1884160 z^9 + 32768 z^10 + 8192 Pi z^(19/2) (-231 + 4 z) StruveL[0, 2 Sqrt[z]]) + 2 Sqrt[z] BesselI[0, 2 Sqrt[z]] (-4298468674500 - 821766070125 z + 25285109850 z^2 + 1728896400 z^3 + 104781600 z^4 + 8467200 z^5 + 1128960 z^6 + 331776 z^7 + 466944 z^8 - 1900544 z^9 + 32768 z^10 + 4096 Pi z^9 (-231 + 4 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]