Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.2011)

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=-3/2, b_1`>=-11/2

For fixed z and a₁=-3/2, b₁=9/2

http://functions.wolfram.com/07.22.03.2011.01

Input Form

HypergeometricPFQ[{-(3/2)}, {9/2, 6}, z] == (1/(164736 z^(9/2))) (4 (2 Sqrt[z] (-138240 + 380160 z + 361125 z^2 + 139440 z^3 + 71712 z^4 - 12544 z^5 + 256 z^6) BesselI[0, 2 Sqrt[z]] - (-276480 + 622080 z + 449775 z^2 + 165480 z^3 + 65664 z^4 - 12416 z^5 + 256 z^6) BesselI[1, 2 Sqrt[z]]) - Pi z^(3/2) (2027025 + 1621620 z + 617760 z^2 + 274560 z^3 - 49920 z^4 + 1024 z^5) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi z^(3/2) (2027025 + 1621620 z + 617760 z^2 + 274560 z^3 - 49920 z^4 + 1024 z^5) BesselI[0, 2 Sqrt[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]