Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9666)

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/07.22.03.9666.01

Input Form

HypergeometricPFQ[{-(19/4)}, {11/2, 17/4}, z] == (4 (-4566533013504000 - 9133066027008000 Sqrt[z] + 39141711544320000 z - 19080256625805375 z^(3/2) + 53654909012189100 z^2 - 14388178781869200 z^(5/2) + 44391315126312000 z^3 - 13536289898208000 z^(7/2) + 66578967100800000 z^4 + 5222705014517760 z^(9/2) - 21989880841420800 z^5 - 398159372943360 z^(11/2) + 1622082433843200 z^6 + 10129417175040 z^(13/2) - 40797210673152 z^7 - 94103404544 z^(15/2) + 377218924544 z^8 + 268435456 z^(17/2) - 1073741824 z^9 + E^(4 Sqrt[z]) (4566533013504000 - 9133066027008000 Sqrt[z] - 39141711544320000 z - 19080256625805375 z^(3/2) - 53654909012189100 z^2 - 14388178781869200 z^(5/2) - 44391315126312000 z^3 - 13536289898208000 z^(7/2) - 66578967100800000 z^4 + 5222705014517760 z^(9/2) + 21989880841420800 z^5 - 398159372943360 z^(11/2) - 1622082433843200 z^6 + 10129417175040 z^(13/2) + 40797210673152 z^7 - 94103404544 z^(15/2) - 377218924544 z^8 + 268435456 z^(17/2) + 1073741824 z^9)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(5/4) (109541101083789375 + 173101986897840000 z + 149134019481216000 z^2 + 280722860199936000 z^3 - 89118368317440000 z^4 + 6518372082647040 z^5 - 163470146273280 z^6 + 1509681004544 z^7 - 4294967296 z^8) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(5/4) (109541101083789375 + 173101986897840000 z + 149134019481216000 z^2 + 280722860199936000 z^3 - 89118368317440000 z^4 + 6518372082647040 z^5 - 163470146273280 z^6 + 1509681004544 z^7 - 4294967296 z^8) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(904878957055180800 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]