Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8916)

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/07.22.03.8916.01

Input Form

HypergeometricPFQ[{-(21/4)}, {5/2, -(13/4)}, z] == (1/(127556629200 z^(3/2))) ((13749310575 - 13749310575 E^(4 Sqrt[z]) + 27498621150 Sqrt[z] + 27498621150 E^(4 Sqrt[z]) Sqrt[z] - 11578366800 z + 11578366800 E^(4 Sqrt[z]) z + 3956752800 z^(3/2) + 3956752800 E^(4 Sqrt[z]) z^(3/2) - 1349187840 z^2 + 1349187840 E^(4 Sqrt[z]) z^2 + 494968320 z^(5/2) + 494968320 E^(4 Sqrt[z]) z^(5/2) - 205148160 z^3 + 205148160 E^(4 Sqrt[z]) z^3 + 100638720 z^(7/2) + 100638720 E^(4 Sqrt[z]) z^(7/2) - 61931520 z^4 + 61931520 E^(4 Sqrt[z]) z^4 + 52297728 z^(9/2) + 52297728 E^(4 Sqrt[z]) z^(9/2) - 72351744 z^5 + 72351744 E^(4 Sqrt[z]) z^5 + 295698432 z^(11/2) + 295698432 E^(4 Sqrt[z]) z^(11/2) + 2097152 z^6 - 2097152 E^(4 Sqrt[z]) z^6 - 8388608 z^(13/2) - 8388608 E^(4 Sqrt[z]) z^(13/2) - 524288 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(23/4) (-567 + 16 z) Erf[Sqrt[2] z^(1/4)] + 524288 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(23/4) (-567 + 16 z) 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]