Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7z7)

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`=-9/2

http://functions.wolfram.com/07.22.03.a7z7.01

Input Form

HypergeometricPFQ[{-(15/4)}, {-(9/2), 17/4}, -z] == (13 (Sqrt[Pi] (65872573680375 + 26443470438000 z + 9402122822400 z^2 + 10901011968000 z^3 - 3059933184000 z^4 + 279765319680 z^5 - 12331253760 z^6 + 268435456 z^7) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((65872573680375 - 43820608154400 z - 959400288000 z^2 + 211036815360 z^3 - 18269798400 z^4 + 786432000 z^5 - 16777216 z^6) Cos[2 Sqrt[z]] + 4 Sqrt[z] (21957524560125 - 1223235367200 z + 726818400000 z^2 - 194883010560 z^3 + 17636720640 z^4 - 773849088 z^5 + 16777216 z^6) Sin[2 Sqrt[z]])))/ (151526446202880 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]