Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9a0)

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.a9a0.01

Input Form

HypergeometricPFQ[{-(9/4)}, {-(11/2), 23/4}, z] == (19 (4 z^(1/4) (-26264240610733125 - 35018987480977500 Sqrt[z] - 23232108767868000 z - 9631238368752000 z^(3/2) - 2577113617478400 z^2 - 423990235468800 z^(5/2) - 36931287859200 z^3 + 1882821427200 z^(7/2) - 301916160000 z^4 + 1161004056576 z^(9/2) - 14803795968 z^5 + 58560872448 z^(11/2) - 218103808 z^6 + 872415232 z^(13/2) + E^(4 Sqrt[z]) (26264240610733125 - 35018987480977500 Sqrt[z] + 23232108767868000 z - 9631238368752000 z^(3/2) + 2577113617478400 z^2 - 423990235468800 z^(5/2) + 36931287859200 z^3 + 1882821427200 z^(7/2) + 301916160000 z^4 + 1161004056576 z^(9/2) + 14803795968 z^5 + 58560872448 z^(11/2) + 218103808 z^6 + 872415232 z^(13/2))) + 13 E^(2 Sqrt[z]) Sqrt[2 Pi] (2020326200825625 - 367929324378000 z + 43392156192000 z^2 - 5009195520000 z^3 + 921231360000 z^4 + 353752842240 z^5 + 17968398336 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] - 13 E^(2 Sqrt[z]) Sqrt[2 Pi] (2020326200825625 - 367929324378000 z + 43392156192000 z^2 - 5009195520000 z^3 + 921231360000 z^4 + 353752842240 z^5 + 17968398336 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/(738871813865472 z^(19/4))

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]