Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9000)

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`=7/2

http://functions.wolfram.com/07.22.03.9000.01

Input Form

HypergeometricPFQ[{-(21/4)}, {7/2, 23/4}, z] == (-4 z^(1/4) (-4585719216759305625 - 6114292289012407500 Sqrt[z] + 4891433831209926000 z + 10248718503487464000 z^(3/2) - 591027408610329600 z^2 + 28632399011106508800 z^(5/2) - 1148670992222208000 z^3 + 33249139103519539200 z^(7/2) + 16328329349146214400 z^4 - 73432826588894330880 z^(9/2) - 3207994231027138560 z^5 + 13327491360463257600 z^(11/2) + 176590057698754560 z^6 - 716830099416023040 z^(13/2) - 3583532806963200 z^7 + 14417109996011520 z^(15/2) + 27895812587520 z^8 - 111789408780288 z^(17/2) - 68719476736 z^9 + 274877906944 z^(19/2) + E^(4 Sqrt[z]) (4585719216759305625 - 6114292289012407500 Sqrt[z] - 4891433831209926000 z + 10248718503487464000 z^(3/2) + 591027408610329600 z^2 + 28632399011106508800 z^(5/2) + 1148670992222208000 z^3 + 33249139103519539200 z^(7/2) - 16328329349146214400 z^4 - 73432826588894330880 z^(9/2) + 3207994231027138560 z^5 + 13327491360463257600 z^(11/2) - 176590057698754560 z^6 - 716830099416023040 z^(13/2) + 3583532806963200 z^7 + 14417109996011520 z^(15/2) - 27895812587520 z^8 - 111789408780288 z^(17/2) + 68719476736 z^9 + 274877906944 z^(19/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] (4585719216759305625 - 9782867662419852000 z + 64033315608566304000 z^2 + 130099434887245824000 z^3 + 173465913182994432000 z^4 - 302776866646681190400 z^5 + 53826998514965544960 z^6 - 2877968174567915520 z^7 + 57751869723770880 z^8 - 447363793551360 z^9 + 1099511627776 z^10) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (4585719216759305625 - 9782867662419852000 z + 64033315608566304000 z^2 + 130099434887245824000 z^3 + 173465913182994432000 z^4 - 302776866646681190400 z^5 + 53826998514965544960 z^6 - 2877968174567915520 z^7 + 57751869723770880 z^8 - 447363793551360 z^9 + 1099511627776 z^10) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/ (1280161915985178132480 z^(19/4))

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]