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

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`=-5/2

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

Input Form

HypergeometricPFQ[{19/4}, {-(5/2), -(15/4)}, z] == -((1/(180093375 z^(1/4))) (Sqrt[2] (3 (-60031125 + 89646480 z - 388080 z^2 - 51448320 z^3 + 364277760 z^4 + 706478080 z^5 + 18874368 z^6) BesselI[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (-180093375 + 28814940 z + 82993680 z^2 - 62092800 z^3 + 993484800 z^4 + 246546432 z^5 + 1048576 z^6) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 12 z (-60031125 - 70436520 z - 51004800 z^2 - 74511360 z^3 + 118292480 z^4 + 4456448 z^5) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^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]