Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8m0)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=1/2

http://functions.wolfram.com/07.22.03.a8m0.01

Input Form

HypergeometricPFQ[{-(13/4)}, {1/2, 23/4}, z] == -((19 (4 z^(1/4) (4656674397375 + 6208899196500 Sqrt[z] + 2629651424400 z - 278269992000 z^(3/2) - 316436440320 z^2 + 254477583360 z^(5/2) + 19372953600 z^3 - 254615961600 z^(7/2) + 309967257600 z^4 - 1814175154176 z^(9/2) - 247502733312 z^5 + 1044067123200 z^(11/2) + 18941476864 z^6 - 76571213824 z^(13/2) - 268435456 z^7 + 1073741824 z^(15/2) + E^(4 Sqrt[z]) (-4656674397375 + 6208899196500 Sqrt[z] - 2629651424400 z - 278269992000 z^(3/2) + 316436440320 z^2 + 254477583360 z^(5/2) - 19372953600 z^3 - 254615961600 z^(7/2) - 309967257600 z^4 - 1814175154176 z^(9/2) + 247502733312 z^5 + 1044067123200 z^(11/2) - 18941476864 z^6 - 76571213824 z^(13/2) + 268435456 z^7 + 1073741824 z^(15/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-4656674397375 + 2337467932800 z - 915372057600 z^2 + 464950886400 z^3 - 619934515200 z^4 - 7935161794560 z^5 + 4232086290432 z^6 - 307090161664 z^7 + 4294967296 z^8) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (-4656674397375 + 2337467932800 z - 915372057600 z^2 + 464950886400 z^3 - 619934515200 z^4 - 7935161794560 z^5 + 4232086290432 z^6 - 307090161664 z^7 + 4294967296 z^8) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/(369435906932736 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]