Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0533)

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/07.22.03.0533.01

Input Form

HypergeometricPFQ[{-(11/2)}, {1, 3}, z] == (1/(21070924875 z)) (4 (z (5294745225 - 18430335000 z + 10152440640 z^2 - 1396126080 z^3 + 61505280 z^4 - 930816 z^5 + 4096 z^6) BesselI[0, Sqrt[z]]^2 + Sqrt[z] (-108056025 + 12656120400 z - 9200230560 z^2 + 1351526400 z^3 - 60814080 z^4 + 927744 z^5 - 4096 z^6) BesselI[0, Sqrt[z]] BesselI[1, Sqrt[z]] + (108056025 - 756392175 z + 14235984360 z^2 - 9497746080 z^3 + 1366058880 z^4 - 61042944 z^5 + 928768 z^6 - 4096 z^7) BesselI[1, Sqrt[z]]^2))

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]