Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1203)

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=-7/2, b_1`>=-11/2

For fixed z and a₁=-7/2, b₁=1/2

http://functions.wolfram.com/07.22.03.1203.01

Input Form

HypergeometricPFQ[{-(7/2)}, {1/2, 5}, z] == (1/(2027025 z^(7/2))) (8 (-2 BesselI[1, 2 Sqrt[z]] (99225 + 28350 z - 25200 z^3 - 207360 z^4 + 80676 z^5 - 5024 z^6 + 64 z^7 + Pi z^(9/2) (-225225 + 81900 z - 5040 z^2 + 64 z^3) StruveL[0, 2 Sqrt[z]]) + Sqrt[z] BesselI[0, 2 Sqrt[z]] (198450 - 42525 z + 37800 z^2 + 176400 z^3 - 979200 z^4 + 332592 z^5 - 20224 z^6 + 256 z^7 + 2 Pi z^4 (-225225 + 81900 z - 5040 z^2 + 64 z^3) 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]