Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8985)

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`=7/2

http://functions.wolfram.com/07.22.03.8985.01

Input Form

HypergeometricPFQ[{-(21/4)}, {7/2, 7/4}, -z] == (Sqrt[Pi] z^(7/4) (12604189422825 + 110000198599200 z + 58666772586240 z^2 + 7319051550720 z^3 + 293741199360 z^4 + 4095737856 z^5 + 16777216 z^6) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 (4 Sqrt[z] (43306099200 + 269460172800 z + 6335804379555 z^2 + 3587815924560 z^3 + 454100774400 z^4 + 18311258112 z^5 + 255787008 z^6 + 1048576 z^7) Cos[2 Sqrt[z]] + (-86612198400 - 423437414400 z + 4641261636375 z^2 + 3297698444880 z^3 + 441139668480 z^4 + 18122711040 z^5 + 255000576 z^6 + 1048576 z^7) Sin[2 Sqrt[z]]))/(83059643842560 z^(5/2))

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]