Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7uw)

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`=9/2

http://functions.wolfram.com/07.22.03.a7uw.01

Input Form

HypergeometricPFQ[{-(17/4)}, {9/2, 7/4}, z] == (1/(988805283840 z^(7/2))) ((4 (-751842000 - 1503684000 Sqrt[z] - 171849600 z + 1661212800 z^(3/2) - 1833062400 z^2 - 6415718400 z^(5/2) - 13870739025 z^3 + 68832073620 z^(7/2) + 5720172480 z^4 - 24167639040 z^(9/2) - 463664640 z^5 + 1886177280 z^(11/2) + 10731520 z^6 - 43122688 z^(13/2) - 65536 z^7 + 262144 z^(15/2) + E^(4 Sqrt[z]) (751842000 - 1503684000 Sqrt[z] + 171849600 z + 1661212800 z^(3/2) + 1833062400 z^2 - 6415718400 z^(5/2) + 13870739025 z^3 + 68832073620 z^(7/2) - 5720172480 z^4 - 24167639040 z^(9/2) + 463664640 z^5 + 1886177280 z^(11/2) - 10731520 z^6 - 43122688 z^(13/2) + 65536 z^7 + 262144 z^(15/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(11/4) (-54563590575 + 291005816400 z - 98023011840 z^2 + 7576657920 z^3 - 172687360 z^4 + 1048576 z^5) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(11/4) (54563590575 - 291005816400 z + 98023011840 z^2 - 7576657920 z^3 + 172687360 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]