Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0543)

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/07.22.03.0543.01

Input Form

HypergeometricPFQ[{-(11/2)}, {1, 11/2}, z] == (1/(20927899238400 z^4)) (4 (2 z (-397105891875 + 218273170500 z - 159058468800 z^2 + 2839481568000 z^3 - 7576723560960 z^4 + 2639530874880 z^5 - 237843824640 z^6 + 7245856768 z^7 - 79364096 z^8 + 262144 z^9) BesselI[0, 2 Sqrt[z]] + Sqrt[z] (1191317675625 - 443029702500 z + 352694865600 z^2 - 580909190400 z^3 + 6436017169920 z^4 - 2526602803200 z^5 + 234289152000 z^6 - 7206404096 z^7 + 79233024 z^8 - 262144 z^9) BesselI[1, 2 Sqrt[z]]) + Pi (-1191317675625 + 972504225000 z - 700203042000 z^2 + 829870272000 z^3 - 5809091904000 z^4 + 27883641139200 z^5 - 10327274496000 z^6 + 944207953920 z^7 - 28904325120 z^8 + 317194240 z^9 - 1048576 z^10) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi (1191317675625 - 972504225000 z + 700203042000 z^2 - 829870272000 z^3 + 5809091904000 z^4 - 27883641139200 z^5 + 10327274496000 z^6 - 944207953920 z^7 + 28904325120 z^8 - 317194240 z^9 + 1048576 z^10) 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]