Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0883)

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=-9/2, b_1`>=-11/2

For fixed z and a₁=-9/2, b₁=1

http://functions.wolfram.com/07.22.03.0883.01

Input Form

HypergeometricPFQ[{-(9/2)}, {1, 5}, z] == -((1/(10854718875 z^3)) (16 (z (-32148900 + 22325625 z - 700131600 z^2 + 1510941600 z^3 - 450478080 z^4 + 32649984 z^5 - 706560 z^6 + 4096 z^7) BesselI[0, Sqrt[z]]^2 - 2 Sqrt[z] (-64297800 + 36614025 z - 37507050 z^2 + 610772400 z^3 - 213570720 z^4 + 16063488 z^5 - 351744 z^6 + 2048 z^7) BesselI[0, Sqrt[z]] BesselI[1, Sqrt[z]] + (-128595600 + 57153600 z - 65190825 z^2 + 200037600 z^3 - 1308123360 z^4 + 434670336 z^5 - 32299776 z^6 + 704512 z^7 - 4096 z^8) 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]