Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8bx)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a8bx.01

Input Form

HypergeometricPFQ[{-(15/4)}, {11/2, -(5/4)}, -z] == ((4 z (183635211375 + 22811827500 z + 7604150400 z^2 + 9141580800 z^3 - 6606028800 z^4 + 3999006720 z^5 + 781189120 z^6 + 16777216 z^7) BesselJ[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (550905634125 - 36498924000 z + 4325983200 z^2 + 6759244800 z^3 - 3994214400 z^4 + 1769472000 z^5 + 385351680 z^6 + 8388608 z^7) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (1652716902375 - 424299991500 z + 17481063600 z^2 + 17643225600 z^3 + 44919705600 z^4 - 29326049280 z^5 + 15241052160 z^6 + 3107979264 z^7 + 67108864 z^8) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(20303712000 Sqrt[2] z^(15/4))

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]