Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aem1)

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`=-9/2

http://functions.wolfram.com/07.22.03.aem1.01

Input Form

HypergeometricPFQ[{15/4}, {-(9/2), -(23/4)}, -z] == (1/(330543380475 z^(1/4))) (Sqrt[2] ((330543380475 + 613181923200 z + 131396126400 z^2 - 124582993920 z^3 + 31853606400 z^4 - 6040387584 z^5 - 4662755328 z^6 + 5813305344 z^7 - 33554432 z^8) BesselJ[1/4, Sqrt[z]]^2 - 28 Sqrt[z] (47220482925 + 24636773700 z - 26070660000 z^2 + 7799077440 z^3 - 1463869440 z^4 + 158957568 z^5 - 726663168 z^6 + 54525952 z^7) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 4 z (330543380475 - 268267091400 z + 91247310000 z^2 - 19289128320 z^3 + 3775242240 z^4 - 1801519104 z^5 - 1173356544 z^6 + 8388608 z^7) BesselJ[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]