Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8928)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.8928.01

Input Form

HypergeometricPFQ[{-(21/4)}, {5/2, -(1/4)}, z] == (1/(2616546240 z^(3/2))) ((4 (13157235 + 26314470 Sqrt[z] - 75184200 z + 141613920 z^(3/2) - 318245760 z^2 + 1713374208 z^(5/2) + 201092031 z^3 - 861095340 z^(7/2) - 20753712 z^4 + 84702912 z^(9/2) + 576768 z^5 - 2319360 z^(11/2) - 4096 z^6 + 16384 z^(13/2) + E^(4 Sqrt[z]) (-13157235 + 26314470 Sqrt[z] + 75184200 z + 141613920 z^(3/2) + 318245760 z^2 + 1713374208 z^(5/2) - 201092031 z^3 - 861095340 z^(7/2) + 20753712 z^4 + 84702912 z^(9/2) - 576768 z^5 - 2319360 z^(11/2) + 4096 z^6 + 16384 z^(13/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(11/4) (7392486465 - 3504586176 z + 340526592 z^2 - 9289728 z^3 + 65536 z^4) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(11/4) (-7392486465 + 3504586176 z - 340526592 z^2 + 9289728 z^3 - 65536 z^4) Erfi[Sqrt[2] z^(1/4)])/ E^(2 Sqrt[z]))

Standard Form

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MathML 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]