Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8rj)

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`=11/2

http://functions.wolfram.com/07.22.03.a8rj.01

Input Form

HypergeometricPFQ[{-(13/4)}, {11/2, -(19/4)}, -z] == -(((4 z (151412473587375 + 2598240645000 z + 569036643840 z^2 - 567824302080 z^3 + 54758473728 z^4 - 2090860544 z^5 + 33554432 z^6) BesselJ[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (252354122645625 - 18101076493500 z + 581424480000 z^2 - 309522554880 z^3 + 28318760960 z^4 - 1060110336 z^5 + 16777216 z^6) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (3785311839684375 - 607988310930000 z + 21352814028000 z^2 + 4223681280000 z^3 - 2444210012160 z^4 + 225438597120 z^5 - 8464105472 z^6 + 134217728 z^7) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(941811282720 Sqrt[2] z^(13/4)))

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]