Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9625)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.9625.01

Input Form

HypergeometricPFQ[{-(19/4)}, {9/2, 23/4}, -z] == ((2 Sqrt[z] (-379939855110440625 - 3415840221183390000 z + 4705792839715968000 z^2 - 3293085192619622400 z^3 + 6922707315985612800 z^4 + 1915609631529369600 z^5 + 127473908931624960 z^6 + 2960016298475520 z^7 + 25593710116864 z^8 + 68719476736 z^9) BesselJ[-(1/4), Sqrt[z]]^2 - (-1139819565331321875 - 8510652754473870000 z + 8360777569592448000 z^2 - 5503185725003366400 z^3 + 5908892186256998400 z^4 + 1840623328375603200 z^5 + 125666088745697280 z^6 + 2944135656898560 z^7 + 25550760443904 z^8 + 68719476736 z^9) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (1139819565331321875 - 6006949496449902000 z + 6313676376392985600 z^2 - 4462771073789952000 z^3 + 6488605009487462400 z^4 + 1884851578286899200 z^5 + 126743775899811840 z^6 + 2953644714491904 z^7 + 25576530247680 z^8 + 68719476736 z^9) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (7939833823494144000 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]