Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8617)

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`=-9/2

http://functions.wolfram.com/07.22.03.8617.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(9/2), 23/4}, -z] == -((209 (Sqrt[Pi] (133784276349964865625 + 38568440028818700000 z + 7649938518112800000 z^2 + 1607868851097600000 z^3 + 600271037743104000 z^4 - 548819234507980800 z^5 + 86089291687526400 z^6 - 6727368336998400 z^7 + 344993248051200 z^8 - 14431090114560 z^9 + 1099511627776 z^10) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (44594758783321621875 - 7530028767531270000 z - 32380692140160000 z^2 + 49747737102336000 z^3 - 35608042074931200 z^4 + 5472675377971200 z^5 - 425047747461120 z^6 + 21759378063360 z^7 - 914828034048 z^8 + 68719476736 z^9) Cos[2 Sqrt[z]] + (-133784276349964865625 + 104134788077810490000 z - 2752358831913600000 z^2 + 158954555934720000 z^3 - 42984286765056000 z^4 + 5920247041228800 z^5 - 446271596789760 z^6 + 22661321195520 z^7 - 966367641600 z^8 + 68719476736 z^9) Sin[2 Sqrt[z]])))/(191515574153930342400 z^(19/4)))

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]