Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9546)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.9546.01

Input Form

HypergeometricPFQ[{-(19/4)}, {7/2, -(7/4)}, z] == (1/(13566571200 z^(5/2))) ((-1964187225 + 1964187225 E^(4 Sqrt[z]) - 3928374450 Sqrt[z] - 3928374450 E^(4 Sqrt[z]) Sqrt[z] - 1694592900 z + 1694592900 E^(4 Sqrt[z]) z + 1848646800 z^(3/2) + 1848646800 E^(4 Sqrt[z]) z^(3/2) - 1137628800 z^2 + 1137628800 E^(4 Sqrt[z]) z^2 + 646410240 z^(5/2) + 646410240 E^(4 Sqrt[z]) z^(5/2) - 392555520 z^3 + 392555520 E^(4 Sqrt[z]) z^3 + 280719360 z^(7/2) + 280719360 E^(4 Sqrt[z]) z^(7/2) - 263454720 z^4 + 263454720 E^(4 Sqrt[z]) z^4 + 391249920 z^(9/2) + 391249920 E^(4 Sqrt[z]) z^(9/2) - 1666449408 z^5 + 1666449408 E^(4 Sqrt[z]) z^5 - 35618816 z^(11/2) - 35618816 E^(4 Sqrt[z]) z^(11/2) + 144048128 z^6 - 144048128 E^(4 Sqrt[z]) z^6 + 524288 z^(13/2) + 524288 E^(4 Sqrt[z]) z^(13/2) - 2097152 z^7 + 2097152 E^(4 Sqrt[z]) z^7 - 8192 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(21/4) (206625 - 17632 z + 256 z^2) Erf[Sqrt[2] z^(1/4)] - 8192 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(21/4) (206625 - 17632 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]