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

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=21/4, b_1`>=-11/2

For fixed z and a₁=21/4, b_1`=-11/2

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

Input Form

HypergeometricPFQ[{21/4}, {-(11/2), 15/4}, z] == (1/(7332249600 Sqrt[2] z^(9/4))) ((2 Sqrt[z] (104928949125 + 138088314000 z + 56443046400 z^2 + 14583029760 z^3 - 518062080 z^4 - 143654912 z^5 + 4194304 z^6) BesselI[-(1/4), Sqrt[z]]^2 + (-314786847375 - 893940138000 z - 450704217600 z^2 - 147867033600 z^3 - 11882004480 z^4 + 2444230656 z^5 + 4194304 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 Sqrt[z] (314786847375 + 222394863600 z + 78592550400 z^2 + 15698534400 z^3 - 858193920 z^4 - 143130624 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]