Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9085)

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`=11/2

http://functions.wolfram.com/07.22.03.9085.01

Input Form

HypergeometricPFQ[{-(21/4)}, {11/2, 11/4}, -z] == (Sqrt[Pi] z^(11/4) (-4692195971497125 + 11678354417948400 z + 29503211161132800 z^2 + 6841324327219200 z^3 + 450457568870400 z^4 + 10730502881280 z^5 + 96183779328 z^6 + 268435456 z^7) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 (4 Sqrt[z] (-74269960128000 - 68712344064000 z - 206945412710400 z^2 + 505388803271625 z^3 + 1773799741677600 z^4 + 422564307459840 z^5 + 28030273044480 z^6 + 669536157696 z^7 + 6008340480 z^8 + 16777216 z^9) Cos[2 Sqrt[z]] + (148539920256000 - 60628538880000 z + 177843714048000 z^2 - 67548520842075 z^3 + 1527832864303200 z^4 + 403474928613120 z^5 + 27546494976000 z^6 + 665082593280 z^7 + 5995757568 z^8 + 16777216 z^9) Sin[2 Sqrt[z]]))/ (28794009865420800 z^(9/2))

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]