Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8286)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=3/2

http://functions.wolfram.com/07.22.03.8286.01

Input Form

HypergeometricPFQ[{-(23/4)}, {3/2, -(19/4)}, z] == (1/(1374931057500 Sqrt[z])) ((-316234143225 + 316234143225 E^(4 Sqrt[z]) + 54997242300 Sqrt[z] + 54997242300 E^(4 Sqrt[z]) Sqrt[z] - 10475665200 z + 10475665200 E^(4 Sqrt[z]) z + 2205403200 z^(3/2) + 2205403200 E^(4 Sqrt[z]) z^(3/2) - 518918400 z^2 + 518918400 E^(4 Sqrt[z]) z^2 + 138378240 z^(5/2) + 138378240 E^(4 Sqrt[z]) z^(5/2) - 42577920 z^3 + 42577920 E^(4 Sqrt[z]) z^3 + 15482880 z^(7/2) + 15482880 E^(4 Sqrt[z]) z^(7/2) - 6881280 z^4 + 6881280 E^(4 Sqrt[z]) z^4 + 3932160 z^(9/2) + 3932160 E^(4 Sqrt[z]) z^(9/2) - 3145728 z^5 + 3145728 E^(4 Sqrt[z]) z^5 + 4194304 z^(11/2) + 4194304 E^(4 Sqrt[z]) z^(11/2) - 16777216 z^6 + 16777216 E^(4 Sqrt[z]) z^6 - 16777216 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(25/4) Erf[Sqrt[2] z^(1/4)] - 16777216 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(25/4) 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]