Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aa46)

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=-7/4, b_1`>=-11/2

For fixed z and a₁=-7/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.aa46.01

Input Form

HypergeometricPFQ[{-(7/4)}, {11/2, 5/4}, z] == (1/(5657600 z^(9/2))) ((1289925 - 1289925 E^(4 Sqrt[z]) + 2579850 Sqrt[z] + 2579850 E^(4 Sqrt[z]) Sqrt[z] + 1871100 z - 1871100 E^(4 Sqrt[z]) z + 302400 z^(3/2) + 302400 E^(4 Sqrt[z]) z^(3/2) - 226800 z^2 + 226800 E^(4 Sqrt[z]) z^2 + 60480 z^(5/2) + 60480 E^(4 Sqrt[z]) z^(5/2) + 53760 z^3 - 53760 E^(4 Sqrt[z]) z^3 - 215040 z^(7/2) - 215040 E^(4 Sqrt[z]) z^(7/2) + 1290240 z^4 - 1290240 E^(4 Sqrt[z]) z^4 + 171520 z^(9/2) + 171520 E^(4 Sqrt[z]) z^(9/2) - 710656 z^5 + 710656 E^(4 Sqrt[z]) z^5 - 8192 z^(11/2) - 8192 E^(4 Sqrt[z]) z^(11/2) + 32768 z^6 - 32768 E^(4 Sqrt[z]) z^6 + 128 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(17/4) (11025 - 5600 z + 256 z^2) Erf[Sqrt[2] z^(1/4)] + 128 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(17/4) (11025 - 5600 z + 256 z^2) 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]