Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9718)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.9718.01

Input Form

HypergeometricPFQ[{-(17/4)}, {-(11/2), 21/4}, z] == ((-2 Sqrt[z] (-402590414354453325 + 465850841067612000 z - 6453344984486400 z^2 + 1818425726853120 z^3 + 2391934772183040 z^4 + 277293324828672 z^5 + 13597094707200 z^6 + 346281738240 z^7 + 4294967296 z^8) BesselI[1/4, Sqrt[z]]^2 + 3 (-670984023924088875 + 1253562263236483200 z + 154880279627673600 z^2 + 4441011602227200 z^3 + 2657221039226880 z^4 + 289730231009280 z^5 + 13906433015808 z^6 + 350039834624 z^7 + 4294967296 z^8) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (-2012952071772266625 - 533610963404719200 z - 19360034953459200 z^2 + 3936351192883200 z^3 + 2614436922654720 z^4 + 287844964761600 z^5 + 13861033869312 z^6 + 349502963712 z^7 + 4294967296 z^8) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (3867475779256320 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]