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

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=1/4, b_1`>=-11/2

For fixed z and a₁=1/4, b_1`=-11/2

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

Input Form

HypergeometricPFQ[{1/4}, {-(11/2), 17/4}, z] == (1/(62008590336 z^(13/4))) ((13 (4 z^(1/4) (665379532125 + 887172709500 Sqrt[z] + 608347000800 z + 270376444800 z^(3/2) + 82566570240 z^2 + 17700387840 z^(5/2) + 2393899008 z^3 + 205520896 z^(7/2) + 8388608 z^4 + E^(4 Sqrt[z]) (665379532125 - 887172709500 Sqrt[z] + 608347000800 z - 270376444800 z^(3/2) + 82566570240 z^2 - 17700387840 z^(5/2) + 2393899008 z^3 - 205520896 z^(7/2) + 8388608 z^4)) + 504735 E^(2 Sqrt[z]) Sqrt[2 Pi] (-1318275 + 200880 z - 20736 z^2 + 4096 z^3) Erf[Sqrt[2] z^(1/4)] + 504735 E^(2 Sqrt[z]) Sqrt[2 Pi] (-1318275 + 200880 z - 20736 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]