Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ael1)

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=15/4, b_1`>=-11/2

For fixed z and a₁=15/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.ael1.01

Input Form

HypergeometricPFQ[{15/4}, {-(11/2), -(11/4)}, -z] == (1/(554687595 z^(1/4))) (Sqrt[2] ((554687595 + 971849340 z + 136216080 z^2 - 215107200 z^3 - 47013120 z^4 - 186224640 z^5 - 111607808 z^6 + 1048576 z^7) BesselJ[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (-554687595 - 232265880 z + 314344800 z^2 - 110880000 z^3 + 84102144 z^4 - 31457280 z^5 + 9699328 z^6) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] - 4 z (-554687595 + 507317580 z - 221205600 z^2 + 89369280 z^3 - 55329792 z^4 - 20824064 z^5 + 262144 z^6) 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]