Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8qm)

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`=9/2

http://functions.wolfram.com/07.22.03.a8qm.01

Input Form

HypergeometricPFQ[{-(13/4)}, {9/2, -(3/4)}, z] == (1/(28034424 Sqrt[2] z^(9/4))) ((-4 z (-10472085 - 9691488 z + 11872512 z^2 + 33472512 z^3 - 8798208 z^4 + 262144 z^5) BesselI[1/4, Sqrt[z]]^2 + 12 Sqrt[z] (-17453475 + 5658120 z + 14943744 z^2 + 13080576 z^3 - 4284416 z^4 + 131072 z^5) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + (261802125 - 61600500 z + 47848320 z^2 + 116425728 z^3 + 108527616 z^4 - 34406400 z^5 + 1048576 z^6) 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]