Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9239)

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`=-7/2

http://functions.wolfram.com/07.22.03.9239.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(7/2), 21/4}, -z] == (221 (Sqrt[Pi] (48811577097157875 + 17441357573178000 z + 4593608578944000 z^2 + 1491258437222400 z^3 + 1883694868070400 z^4 - 669758175313920 z^5 + 92780353290240 z^6 - 8262443335680 z^7 + 734439407616 z^8 + 68719476736 z^9) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((-(-48811577097157875 + 34624324663790400 z + 787475756390400 z^2 + 163236081254400 z^3 - 48458565550080 z^4 + 6310644940800 z^5 - 543581798400 z^6 + 41875931136 z^7 + 4294967296 z^8)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (16270525699052625 - 1624168747555200 z + 75565855411200 z^2 + 128006599311360 z^3 - 43142611599360 z^4 + 5903524823040 z^5 - 523247812608 z^6 + 45097156608 z^7 + 4294967296 z^8) Sin[2 Sqrt[z]])))/ (465489242735247360 z^(17/4))

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]