Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8398)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.8398.01

Input Form

HypergeometricPFQ[{-(23/4)}, {7/2, -(3/4)}, z] == (1/(191870078400 z^(5/2))) ((-7972289325 + 7972289325 E^(4 Sqrt[z]) - 15944578650 Sqrt[z] - 15944578650 E^(4 Sqrt[z]) Sqrt[z] - 2453012100 z + 2453012100 E^(4 Sqrt[z]) z + 16353414000 z^(3/2) + 16353414000 E^(4 Sqrt[z]) z^(3/2) - 21804552000 z^2 + 21804552000 E^(4 Sqrt[z]) z^2 + 24852199680 z^(5/2) + 24852199680 E^(4 Sqrt[z]) z^(5/2) - 31699261440 z^3 + 31699261440 E^(4 Sqrt[z]) z^3 + 57626173440 z^(7/2) + 57626173440 E^(4 Sqrt[z]) z^(7/2) - 276634828800 z^4 + 276634828800 E^(4 Sqrt[z]) z^4 - 18957074400 z^(9/2) - 18957074400 E^(4 Sqrt[z]) z^(9/2) + 79372047744 z^5 - 79372047744 E^(4 Sqrt[z]) z^5 + 1261905408 z^(11/2) + 1261905408 E^(4 Sqrt[z]) z^(11/2) - 5120514048 z^6 + 5120514048 E^(4 Sqrt[z]) z^6 - 24748032 z^(13/2) - 24748032 E^(4 Sqrt[z]) z^(13/2) + 99385344 z^7 - 99385344 E^(4 Sqrt[z]) z^7 + 131072 z^(15/2) + 131072 E^(4 Sqrt[z]) z^(15/2) - 524288 z^8 + 524288 E^(4 Sqrt[z]) z^8 - 8 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(17/4) (36227354625 - 10037016000 z + 642369024 z^2 - 12435456 z^3 + 65536 z^4) Erf[Sqrt[2] z^(1/4)] - 8 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(17/4) (36227354625 - 10037016000 z + 642369024 z^2 - 12435456 z^3 + 65536 z^4) Erfi[Sqrt[2] z^(1/4)])/ E^(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]