Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9oc)

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=-9/4, b_1`>=-11/2

For fixed z and a₁=-9/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a9oc.01

Input Form

HypergeometricPFQ[{-(9/4)}, {11/2, 11/4}, z] == (1/(1417641984 z^(9/2))) ((7 (4 (-2381400 - 4762800 Sqrt[z] - 2138400 z + 2073600 z^(3/2) - 362880 z^2 - 5184000 z^(5/2) + 392175 z^3 - 6849900 z^(7/2) - 2464560 z^4 + 10550976 z^(9/2) + 244992 z^5 - 992256 z^(11/2) - 4096 z^6 + 16384 z^(13/2) + E^(4 Sqrt[z]) (2381400 - 4762800 Sqrt[z] + 2138400 z + 2073600 z^(3/2) + 362880 z^2 - 5184000 z^(5/2) - 392175 z^3 - 6849900 z^(7/2) + 2464560 z^4 + 10550976 z^(9/2) - 244992 z^5 - 992256 z^(11/2) + 4096 z^6 + 16384 z^(13/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(11/4) (-23892975 - 33981120 z + 42923520 z^2 - 3981312 z^3 + 65536 z^4) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(11/4) (23892975 + 33981120 z - 42923520 z^2 + 3981312 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]