Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8j3)

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`=-3/2

http://functions.wolfram.com/07.22.03.a8j3.01

Input Form

HypergeometricPFQ[{-(13/4)}, {-(3/2), 13/4}, -z] == (1/(34062336 Sqrt[2] z^(7/4))) ((2 Sqrt[z] (-6081075 + 21521808 z + 17385984 z^2 - 8921088 z^3 + 14745600 z^4 + 1048576 z^5) BesselJ[1/4, Sqrt[z]]^2 + 3 (10135125 + 28108080 z - 40094208 z^2 + 20275200 z^3 - 13828096 z^4 - 1048576 z^5) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (-30405375 - 19459440 z + 35430912 z^2 - 18948096 z^3 + 13959168 z^4 + 1048576 z^5) BesselJ[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]