Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a972)

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

For fixed z and a₁=-11/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a972.01

Input Form

HypergeometricPFQ[{-(11/4)}, {9/2, 13/4}, z] == (1/(17380147200 z^(7/2))) ((4 (-53222400 - 106444800 Sqrt[z] + 425779200 z - 212595075 z^(3/2) + 662715900 z^2 - 251475840 z^(5/2) + 1250430720 z^3 + 98449920 z^(7/2) - 409835520 z^4 - 5570560 z^(9/2) + 22478848 z^5 + 65536 z^(11/2) - 262144 z^6 + E^(4 Sqrt[z]) (53222400 - 106444800 Sqrt[z] - 425779200 z - 212595075 z^(3/2) - 662715900 z^2 - 251475840 z^(5/2) - 1250430720 z^3 + 98449920 z^(7/2) + 409835520 z^4 - 5570560 z^(9/2) - 22478848 z^5 + 65536 z^(11/2) + 262144 z^6)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(5/4) (1206079875 + 2144142000 z + 5277888000 z^2 - 1655808000 z^3 + 90112000 z^4 - 1048576 z^5) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(5/4) (1206079875 + 2144142000 z + 5277888000 z^2 - 1655808000 z^3 + 90112000 z^4 - 1048576 z^5) 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]