Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9647)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.9647.01

Input Form

HypergeometricPFQ[{-(19/4)}, {11/2, -(3/4)}, -z] == (1/(901484812800 z^(9/2))) (-2 Sqrt[z] (4331032831125 - 707107401000 z - 29578348800 z^2 + 91010304000 z^3 - 59463106560 z^4 + 99538698240 z^5 + 16601333760 z^6 + 548929536 z^7 + 4194304 z^8) Cos[2 Sqrt[z]] - 16384 Sqrt[Pi] z^(25/4) (111007215 + 16703280 z + 539904 z^2 + 4096 z^3) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + (4331032831125 - 6481817842500 z - 626691265200 z^2 - 204773184000 z^3 + 141571584000 z^4 - 124570828800 z^5 + 885443788800 z^6 + 136017739776 z^7 + 4416602112 z^8 + 33554432 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]