Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a871)

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`=3/2

http://functions.wolfram.com/07.22.03.a871.01

Input Form

HypergeometricPFQ[{-(15/4)}, {3/2, 11/4}, -z] == ((2 Sqrt[z] (34459425 + 6012349200 z + 8762411520 z^2 + 1862492160 z^3 + 92078080 z^4 + 1048576 z^5) BesselJ[-(1/4), Sqrt[z]]^2 - (103378275 + 2756754000 z + 7740817920 z^2 + 1806704640 z^3 + 91422720 z^4 + 1048576 z^5) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (-103378275 + 4399330320 z + 8330826240 z^2 + 1839882240 z^3 + 91815936 z^4 + 1048576 z^5) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(10081843200 Sqrt[2] z^(5/4))

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]