Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8ki)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=-1/2

http://functions.wolfram.com/07.22.03.a8ki.01

Input Form

HypergeometricPFQ[{-(13/4)}, {-(1/2), 17/4}, z] == ((-2 Sqrt[z] (383107725 - 635675040 z - 877992192 z^2 - 351977472 z^3 + 3279618048 z^4 - 631242752 z^5 + 16777216 z^6) BesselI[1/4, Sqrt[z]]^2 + 3 (638512875 - 1513512000 z + 726485760 z^2 + 1695547392 z^3 + 2752053248 z^4 - 616562688 z^5 + 16777216 z^6) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (1915538625 - 454053600 z + 588107520 z^2 + 1536933888 z^3 + 2822701056 z^4 - 618659840 z^5 + 16777216 z^6) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(1271660544 Sqrt[2] z^(11/4))

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]