Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8355)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.8355.01

Input Form

HypergeometricPFQ[{-(23/4)}, {5/2, 1/4}, -z] == (1/(193808160000 z^(3/2))) (Sqrt[Pi] z^(9/4) (1698294472875 + 1493006130000 z + 255487680000 z^2 + 12977152000 z^3 + 218562560 z^4 + 1048576 z^5) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 ((-Sqrt[z]) (-3634092000 + 57171340800 z + 80920682325 z^2 + 15255863040 z^3 + 798507520 z^4 + 13598720 z^5 + 65536 z^6) Cos[2 Sqrt[z]] + 4 (-454261500 - 4360910400 z + 93519820800 z^2 + 90618912825 z^3 + 15821340480 z^4 + 808537600 z^5 + 13647872 z^6 + 65536 z^7) Sin[2 Sqrt[z]]))

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]