Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8459)

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`=9/2

http://functions.wolfram.com/07.22.03.8459.01

Input Form

HypergeometricPFQ[{-(23/4)}, {9/2, 9/4}, -z] == (Sqrt[Pi] z^(9/4) (-6220852654141125 + 53595038251062000 z + 50442388942176000 z^2 + 9150546746880000 z^3 + 532395447091200 z^4 + 11749416763392 z^5 + 99941875712 z^6 + 268435456 z^7) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 ((-Sqrt[z]) (-146526589440000 - 336034311782400 z + 1719555826544325 z^2 + 2718152104963680 z^3 + 543227609675520 z^4 + 32608777420800 z^5 + 728544509952 z^6 + 6230638592 z^7 + 16777216 z^8) Cos[2 Sqrt[z]] + 4 (-18315823680000 - 17583190732800 z - 500144091955200 z^2 + 2927823368171625 z^3 + 3057383260784160 z^4 + 565956022705920 z^5 + 33139546374144 z^6 + 733174235136 z^7 + 6243221504 z^8 + 16777216 z^9) Sin[2 Sqrt[z]]))/ (58156588243353600 z^(7/2))

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]