Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a88e)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.a88e.01

Input Form

HypergeometricPFQ[{-(15/4)}, {5/2, 13/4}, z] == (1/(2335891783680 z^(9/4))) ((-4 z^(1/4) (3618239625 - 22425549300 Sqrt[z] + 18829918800 z - 123166612800 z^(3/2) - 24474723840 z^2 + 107258296320 z^(5/2) + 3506872320 z^3 - 14385315840 z^(7/2) - 122880000 z^4 + 494665728 z^(9/2) + 1048576 z^5 - 4194304 z^(11/2) + E^(4 Sqrt[z]) (3618239625 + 22425549300 Sqrt[z] + 18829918800 z + 123166612800 z^(3/2) - 24474723840 z^2 - 107258296320 z^(5/2) + 3506872320 z^3 + 14385315840 z^(7/2) - 122880000 z^4 - 494665728 z^(9/2) + 1048576 z^5 + 4194304 z^(11/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (3618239625 + 69470200800 z + 555761606400 z^2 - 439120281600 z^3 + 57905971200 z^4 - 1981808640 z^5 + 16777216 z^6) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (3618239625 + 69470200800 z + 555761606400 z^2 - 439120281600 z^3 + 57905971200 z^4 - 1981808640 z^5 + 16777216 z^6) 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]