Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8400)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.8400.01

Input Form

HypergeometricPFQ[{-(23/4)}, {7/2, -(1/4)}, z] == ((-4 z (110181126825 - 1448029321200 z - 9939043699200 z^2 + 11721213060480 z^3 - 2124289290240 z^4 + 108196134912 z^5 - 1792016384 z^6 + 8388608 z^7) BesselI[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (330543380475 - 503685151200 z - 2586848140800 z^2 + 5277865158720 z^3 - 1029789573120 z^4 + 53545107456 z^5 - 893386752 z^6 + 4194304 z^7) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + (-991630141425 + 1322173521900 z - 7051592116800 z^2 - 30680052480000 z^3 + 44917049802240 z^4 - 8391699283968 z^5 + 431005630464 z^6 - 7159676928 z^7 + 33554432 z^8) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(5036589558000 Sqrt[2] z^(7/4))

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]