Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9mw)

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=-9/4, b_1`>=-11/2

For fixed z and a₁=-9/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a9mw.01

Input Form

HypergeometricPFQ[{-(9/4)}, {9/2, 7/4}, z] == (1/(3691776 z^(7/2))) ((-42525 + 42525 E^(4 Sqrt[z]) - 85050 Sqrt[z] - 85050 E^(4 Sqrt[z]) Sqrt[z] - 29160 z + 29160 E^(4 Sqrt[z]) z + 55080 z^(3/2) + 55080 E^(4 Sqrt[z]) z^(3/2) - 34560 z^2 + 34560 E^(4 Sqrt[z]) z^2 - 172800 z^(5/2) - 172800 E^(4 Sqrt[z]) z^(5/2) - 202500 z^3 + 202500 E^(4 Sqrt[z]) z^3 + 915792 z^(7/2) + 915792 E^(4 Sqrt[z]) z^(7/2) + 38784 z^4 - 38784 E^(4 Sqrt[z]) z^4 - 158208 z^(9/2) - 158208 E^(4 Sqrt[z]) z^(9/2) - 1024 z^5 + 1024 E^(4 Sqrt[z]) z^5 + 4096 z^(11/2) + 4096 E^(4 Sqrt[z]) z^(11/2) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(11/4) (-294975 + 943920 z - 158976 z^2 + 4096 z^3) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(11/4) (294975 - 943920 z + 158976 z^2 - 4096 z^3) 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]