Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9238)

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/07.22.03.9238.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(7/2), 21/4}, z] == -((221 (-4 z^(1/4) (-48811577097157875 - 65082102796210500 Sqrt[z] - 34624324663790400 z - 6496674990220800 z^(3/2) + 787475756390400 z^2 - 302263421644800 z^(5/2) - 163236081254400 z^3 + 512026397245440 z^(7/2) - 48458565550080 z^4 + 172570446397440 z^(9/2) - 6310644940800 z^5 + 23614099292160 z^(11/2) - 543581798400 z^6 + 2092991250432 z^(13/2) - 41875931136 z^7 + 180388626432 z^(15/2) + 4294967296 z^8 - 17179869184 z^(17/2) + E^(4 Sqrt[z]) (-48811577097157875 + 65082102796210500 Sqrt[z] - 34624324663790400 z + 6496674990220800 z^(3/2) + 787475756390400 z^2 + 302263421644800 z^(5/2) - 163236081254400 z^3 - 512026397245440 z^(7/2) - 48458565550080 z^4 - 172570446397440 z^(9/2) - 6310644940800 z^5 - 23614099292160 z^(11/2) - 543581798400 z^6 - 2092991250432 z^(13/2) - 41875931136 z^7 - 180388626432 z^(15/2) + 4294967296 z^8 + 17179869184 z^(17/2))) + E^(2 Sqrt[z]) Sqrt[2 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) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 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) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/ (1861956970940989440 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]