Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9912)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=-3/2

http://functions.wolfram.com/07.22.03.9912.01

Input Form

HypergeometricPFQ[{-(17/4)}, {-(3/2), 23/4}, z] == (209 (4 z^(1/4) (-3778256272415625 - 5037675029887500 Sqrt[z] - 2579289615302400 z - 368469945043200 z^(3/2) + 122078931287040 z^2 - 23820279275520 z^(5/2) - 24143631482880 z^3 + 35517417062400 z^(7/2) - 15192421171200 z^4 + 39461872730112 z^(9/2) - 5387348606976 z^5 + 16390350176256 z^(11/2) - 2549398634496 z^6 + 11003706212352 z^(13/2) + 283467841536 z^7 - 1146756268032 z^(15/2) - 4294967296 z^8 + 17179869184 z^(17/2) + E^(4 Sqrt[z]) (3778256272415625 - 5037675029887500 Sqrt[z] + 2579289615302400 z - 368469945043200 z^(3/2) - 122078931287040 z^2 - 23820279275520 z^(5/2) + 24143631482880 z^3 + 35517417062400 z^(7/2) + 15192421171200 z^4 + 39461872730112 z^(9/2) + 5387348606976 z^5 + 16390350176256 z^(11/2) + 2549398634496 z^6 + 11003706212352 z^(13/2) - 283467841536 z^7 - 1146756268032 z^(15/2) + 4294967296 z^8 + 17179869184 z^(17/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (3778256272415625 - 1450850408607600 z + 401967212774400 z^2 - 126107360870400 z^3 + 77604529766400 z^4 + 137963608473600 z^5 + 58864472948736 z^6 + 44849122246656 z^7 - 4599909974016 z^8 + 68719476736 z^9) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (3778256272415625 - 1450850408607600 z + 401967212774400 z^2 - 126107360870400 z^3 + 77604529766400 z^4 + 137963608473600 z^5 + 58864472948736 z^6 + 44849122246656 z^7 - 4599909974016 z^8 + 68719476736 z^9) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/ (159596311794941952 z^(19/4))

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]