Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7vb)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a7vb.01

Input Form

HypergeometricPFQ[{-(17/4)}, {9/2, 21/4}, -z] == ((2 Sqrt[z] (-1474690162470525 + 14116692153564000 z - 15436993168396800 z^2 + 33135386689658880 z^3 + 24425687242506240 z^4 + 2837390555086848 z^5 + 99708504637440 z^6 + 1205275197440 z^7 + 4294967296 z^8) BesselJ[1/4, Sqrt[z]]^2 - 3 (-2457816937450875 + 21780039322641600 z - 21341033967052800 z^2 + 15379596394905600 z^3 + 22082607810478080 z^4 + 2751897136005120 z^5 + 98660230627328 z^6 + 1201517101056 z^7 + 4294967296 z^8) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (-7373450812352625 + 24922345218170400 z - 22818369298982400 z^2 + 17335993343385600 z^3 + 22392265003499520 z^4 + 2763782671564800 z^5 + 98808776097792 z^6 + 1202053971968 z^7 + 4294967296 z^8) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (21927745974435840 Sqrt[2] z^(15/4))

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]