Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a975)

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`=9/2

http://functions.wolfram.com/07.22.03.a975.01

Input Form

HypergeometricPFQ[{-(11/4)}, {9/2, 15/4}, -z] == ((2 z (2301920775 - 3001244400 z + 7921497600 z^2 + 2064343040 z^3 + 99287040 z^4 + 1048576 z^5) BesselJ[-(1/4), Sqrt[z]]^2 - Sqrt[z] (5368965525 - 5476086000 z + 6785856000 z^2 + 2004049920 z^3 + 98631680 z^4 + 1048576 z^5) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 (-1152597600 + 3851815275 z - 4338457200 z^2 + 7442265600 z^3 + 2039930880 z^4 + 99024896 z^5 + 1048576 z^6) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(9165312000 Sqrt[2] z^(11/4))

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]