Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ae4q)

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=13/4, b_1`>=-11/2

For fixed z and a₁=13/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.ae4q.01

Input Form

HypergeometricPFQ[{13/4}, {-(11/2), -(21/4)}, z] == (1/(97692469875 Sqrt[2])) (z^(1/4) ((97692469875 + 206380629000 z + 140444085600 z^2 + 36088416000 z^3 + 5889300480 z^4 + 903168000 z^5 + 660602880 z^6 + 155189248 z^7) BesselI[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (-97692469875 - 128226653100 z - 44809783200 z^2 - 8503911360 z^3 - 1259919360 z^4 - 237404160 z^5 + 366477312 z^6 + 4194304 z^7) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 36 z (10854718875 + 5563630800 z + 1299851280 z^2 + 205632000 z^3 + 31395840 z^4 + 9175040 z^5 + 4194304 z^6) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^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]