Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aak2)

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=-5/4, b_1`>=-11/2

For fixed z and a₁=-5/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.aak2.01

Input Form

HypergeometricPFQ[{-(5/4)}, {11/2, 1/4}, z] == (1/(153824 Sqrt[2] z^(13/4))) (3 (4 z (-208845 + 34320 z + 15616 z^2 - 69632 z^3 + 16384 z^4) BesselI[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (-348075 + 26260 z - 10560 z^2 - 27648 z^3 + 8192 z^4) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] - (5221125 + 70200 z + 107520 z^2 - 81920 z^3 - 229376 z^4 + 65536 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]