Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9384)

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`=-1/2

http://functions.wolfram.com/07.22.03.9384.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(1/2), 23/4}, z] == ((2 Sqrt[z] (-9290065422763125 - 6134392406142000 z + 1176626715264000 z^2 - 257449947955200 z^3 + 1381571798630400 z^4 + 2630583425433600 z^5 - 3160284919234560 z^6 + 362956948766720 z^7 - 10088878178304 z^8 + 68719476736 z^9) BesselI[-(1/4), Sqrt[z]]^2 + (27870196268289375 + 60872047722486000 z - 5490924671232000 z^2 + 2027418340147200 z^3 - 600716545228800 z^4 - 1158419526451200 z^5 + 2949583554478080 z^6 - 356766827151360 z^7 + 10045928505344 z^8 - 68719476736 z^9) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 Sqrt[z] (27870196268289375 + 1415629016802000 z + 549092467123200 z^2 - 643624869888000 z^3 + 1307441892556800 z^4 + 1965001487155200 z^5 - 3073360149872640 z^6 + 360461572767744 z^7 - 10071698309120 z^8 + 68719476736 z^9) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (3123421013606400 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]