Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7wc)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a7wc.01

Input Form

HypergeometricPFQ[{-(17/4)}, {11/2, 11/4}, z] == (4 (-252618912000 - 505237824000 Sqrt[z] - 144353664000 z + 384943104000 z^(3/2) - 192471552000 z^2 - 1077840691200 z^(5/2) - 19306676025 z^3 - 2215640781900 z^(7/2) - 1375720491600 z^4 + 6230936980800 z^(9/2) + 285348349440 z^5 - 1182647531520 z^(11/2) - 14516920320 z^6 + 58755809280 z^(13/2) + 232980480 z^7 - 935067648 z^(15/2) - 1048576 z^8 + 4194304 z^(17/2) + E^(4 Sqrt[z]) (252618912000 - 505237824000 Sqrt[z] + 144353664000 z + 384943104000 z^(3/2) + 192471552000 z^2 - 1077840691200 z^(5/2) + 19306676025 z^3 - 2215640781900 z^(7/2) + 1375720491600 z^4 + 6230936980800 z^(9/2) - 285348349440 z^5 - 1182647531520 z^(11/2) + 14516920320 z^6 + 58755809280 z^(13/2) - 232980480 z^7 - 935067648 z^(15/2) + 1048576 z^8 + 4194304 z^(17/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(11/4) (-5729177010375 - 12222244288800 z + 25731040608000 z^2 - 4773294489600 z^3 + 235718246400 z^4 - 3743416320 z^5 + 16777216 z^6) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(11/4) (5729177010375 + 12222244288800 z - 25731040608000 z^2 + 4773294489600 z^3 - 235718246400 z^4 + 3743416320 z^5 - 16777216 z^6) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/ (105472563609600 z^(9/2))

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]