Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ag1u)

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=21/4, b_1`>=-11/2

For fixed z and a₁=21/4, b_1`=-5/2

http://functions.wolfram.com/07.22.03.ag1u.01

Input Form

HypergeometricPFQ[{21/4}, {-(5/2), 19/4}, z] == -((1/(217251840 Sqrt[2] z^(13/4))) (77 (2 Sqrt[z] (-402026625 - 494544960 z - 145117440 z^2 - 27262976 z^3 - 4390912 z^4 + 524288 z^5) BesselI[-(1/4), Sqrt[z]]^2 + (1206079875 + 3321470880 z + 1397710080 z^2 + 288178176 z^3 + 54722560 z^4) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 Sqrt[z] (-1206079875 - 748500480 z - 192980736 z^2 - 34996224 z^3 - 4259840 z^4 + 524288 z^5) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2))

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]