Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7w8)

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.a7w8.01

Input Form

HypergeometricPFQ[{-(17/4)}, {11/2, 7/4}, z] == (1/(1922676940800 z^(9/2))) ((4 (7236479250 + 14472958500 Sqrt[z] + 7894341000 z - 3508596000 z^(3/2) - 2506140000 z^2 + 4811788800 z^(5/2) - 3742502400 z^3 - 17108582400 z^(7/2) - 26662196925 z^4 + 127915210500 z^(9/2) + 8790176640 z^5 - 36850302720 z^(11/2) - 602667520 z^6 + 2446366720 z^(13/2) + 12124160 z^7 - 48693248 z^(15/2) - 65536 z^8 + 262144 z^(17/2) + E^(4 Sqrt[z]) (-7236479250 + 14472958500 Sqrt[z] - 7894341000 z - 3508596000 z^(3/2) + 2506140000 z^2 + 4811788800 z^(5/2) + 3742502400 z^3 - 17108582400 z^(7/2) + 26662196925 z^4 + 127915210500 z^(9/2) - 8790176640 z^5 - 36850302720 z^(11/2) + 602667520 z^6 + 2446366720 z^(13/2) - 12124160 z^7 - 48693248 z^(15/2) + 65536 z^8 + 262144 z^(17/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(15/4) (-127315044675 + 536063346000 z - 149165452800 z^2 + 9821593600 z^3 - 194969600 z^4 + 1048576 z^5) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(15/4) (127315044675 - 536063346000 z + 149165452800 z^2 - 9821593600 z^3 + 194969600 z^4 - 1048576 z^5) 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]