Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8447)

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/07.22.03.8447.01

Input Form

HypergeometricPFQ[{-(23/4)}, {9/2, -(3/4)}, -z] == (1/(2028340828800 z^(7/2))) (-2 Sqrt[z] (677644592625 + 138186348300 z + 196240968000 z^2 - 204577781760 z^3 + 420021043200 z^4 + 113085912960 z^5 + 6453958656 z^6 + 111050752 z^7 + 524288 z^8) Cos[2 Sqrt[z]] - 128 Sqrt[Pi] z^(21/4) (63829148625 + 14854783680 z + 819574272 z^2 + 13942784 z^3 + 65536 z^4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + (677644592625 - 765339775200 z - 228947796000 z^2 + 407018304000 z^3 - 484147445760 z^4 + 3926187048960 z^5 + 941226617856 z^6 + 52287160320 z^7 + 891551744 z^8 + 4194304 z^9) 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]