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

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`=9/2

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

Input Form

HypergeometricPFQ[{21/4}, {9/2, -(13/4)}, z] == (1/(24822720 Sqrt[2] z^(11/4))) (7 (4 z (204417675 + 79603920 z + 17149440 z^2 + 5345280 z^3 + 65536 z^4) BesselI[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (-613253025 - 355621860 z - 88208640 z^2 - 22609920 z^3 - 3538944 z^4 + 262144 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 15 (122650605 + 94486392 z + 29975616 z^2 + 6561792 z^3 + 1654784 z^4) 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]