Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a89u)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.a89u.01

Input Form

HypergeometricPFQ[{-(15/4)}, {7/2, 17/4}, z] == (-4 z^(1/4) (814103915625 - 3492506070900 Sqrt[z] + 1843492543200 z - 6051593116800 z^(3/2) + 2574806572800 z^2 - 13470003993600 z^(5/2) - 1375648727040 z^3 + 5826166456320 z^(7/2) + 116699627520 z^4 - 474835845120 z^(9/2) - 2736783360 z^5 + 10997465088 z^(11/2) + 16777216 z^6 - 67108864 z^(13/2) + E^(4 Sqrt[z]) (814103915625 + 3492506070900 Sqrt[z] + 1843492543200 z + 6051593116800 z^(3/2) + 2574806572800 z^2 + 13470003993600 z^(5/2) - 1375648727040 z^3 - 5826166456320 z^(7/2) + 116699627520 z^4 + 474835845120 z^(9/2) - 2736783360 z^5 - 10997465088 z^(11/2) + 16777216 z^6 + 67108864 z^(13/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (814103915625 + 10131070950000 z + 19451656224000 z^2 + 57634536960000 z^3 - 23644938240000 z^4 + 1907490816000 z^5 - 44040192000 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (814103915625 + 10131070950000 z + 19451656224000 z^2 + 57634536960000 z^3 - 23644938240000 z^4 + 1907490816000 z^5 - 44040192000 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(201246061363200 z^(13/4))

Standard Form

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MathML 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]