Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8zd)

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`=-3/2

http://functions.wolfram.com/07.22.03.a8zd.01

Input Form

HypergeometricPFQ[{-(11/4)}, {-(3/2), 23/4}, -z] == (19 (2 Sqrt[z] (-1393022255625 + 1146258313200 z + 61751289600 z^2 + 13099806720 z^3 + 13262192640 z^4 - 5740953600 z^5 + 1426063360 z^6 + 268435456 z^7) BesselJ[-(1/4), Sqrt[z]]^2 - (-4179066766875 + 9806876679600 z - 555761606400 z^2 + 20479979520 z^3 + 16122839040 z^4 - 6181355520 z^5 + 1258291200 z^6 + 268435456 z^7) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (4179066766875 - 891534243600 z + 12350257920 z^2 + 9920655360 z^3 + 14760345600 z^4 - 5992611840 z^5 + 1358954496 z^6 + 268435456 z^7) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (471104225280 Sqrt[2] z^(17/4))

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]