Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7w3)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a7w3.01

Input Form

HypergeometricPFQ[{-(17/4)}, {11/2, 1/4}, -z] == ((4 z (-43616234025 - 15964111800 z + 71413776000 z^2 + 395542425600 z^3 + 283240151040 z^4 + 35089252352 z^5 + 1097334784 z^6 + 8388608 z^7) BesselJ[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (-72693723375 - 20145188700 z - 9824068800 z^2 + 96465868800 z^3 + 127051187200 z^4 + 17070735360 z^5 + 544997376 z^6 + 4194304 z^7) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (-1090405850625 - 205252866000 z - 117187106400 z^2 - 116017574400 z^3 + 858190233600 z^4 + 1031912448000 z^5 + 137098035200 z^6 + 4364173312 z^7 + 33554432 z^8) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(157719592800 Sqrt[2] z^(13/4))

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]