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

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

For fixed z and a₁=11/4, b_1`=-11/2

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

Input Form

HypergeometricPFQ[{11/4}, {-(11/2), -(23/4)}, z] == (1/(330543380475 z^(1/4))) (Sqrt[2] ((330543380475 - 632343858300 z + 165397755600 z^2 + 119357884800 z^3 + 24570120960 z^4 + 3145089024 z^5 + 423886848 z^6 + 968884224 z^7 + 16777216 z^8) BesselI[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (330543380475 - 191619351000 z - 174042237600 z^2 - 43682284800 z^3 - 6308628480 z^4 - 715309056 z^5 + 121634816 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 4 z (330543380475 + 249105156300 z + 74150445600 z^2 + 12271089600 z^3 + 1518612480 z^4 + 211943424 z^5 + 154140672 z^6 + 4194304 z^7) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^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]