Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a99z)

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=-9/4, b_1`>=-11/2

For fixed z and a₁=-9/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.a99z.01

Input Form

HypergeometricPFQ[{-(9/4)}, {-(11/2), 21/4}, -z] == (221 (2 Sqrt[z] (-15569881051725 - 17033716022400 z + 973355201280 z^2 - 36832739328 z^3 + 18129420288 z^4 - 1031798784 z^5 + 16777216 z^6) BesselJ[1/4, Sqrt[z]]^2 + 3 (25949801752875 + 46842719061600 z - 9192799123200 z^2 + 223278612480 z^3 - 19057016832 z^4 + 1046478848 z^5 - 16777216 z^6) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (-77849405258625 + 25550574033600 z - 1622258668800 z^2 - 40596111360 z^3 + 18919784448 z^4 - 1044381696 z^5 + 16777216 z^6) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (7161992183808 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]