Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8561)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.8561.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(11/2), 15/4}, -z] == ((-Sqrt[Pi]) (21913886380010625 + 12142759552560000 z + 7816029137280000 z^2 - 10004517295718400 z^3 + 1905622342041600 z^4 - 159424614236160 z^5 + 7546727301120 z^6 - 225485783040 z^7 + 4294967296 z^8) FresnelS[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) (4 Sqrt[z] (7304628793336875 + 708327640566000 z - 653501182521600 z^2 + 121207180308480 z^3 - 10058938122240 z^4 + 474422968320 z^5 - 14143193088 z^6 + 268435456 z^7) Cos[2 Sqrt[z]] + (-21913886380010625 + 11232052586118000 z - 800212506912000 z^2 + 130789906329600 z^3 - 10467108126720 z^4 + 485873418240 z^5 - 14344519680 z^6 + 268435456 z^7) Sin[2 Sqrt[z]]))/ (15585577323724800 z^(11/4))

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]