Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.adp1)

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

For fixed z and a₁=11/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.adp1.01

Input Form

HypergeometricPFQ[{11/4}, {-(11/2), -(11/4)}, -z] == (1/(50426145 z^(1/4))) (Sqrt[2] ((50426145 + 91683900 z + 17463600 z^2 - 19071360 z^3 + 887040 z^4 - 7053312 z^5 - 2818048 z^6) BesselJ[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (-50426145 - 24449040 z + 27941760 z^2 - 8870400 z^3 + 4053504 z^4 - 1622016 z^5 + 131072 z^6) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 4 z (50426145 - 42785820 z + 16299360 z^2 - 5100480 z^3 + 2537472 z^4 + 606208 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]