Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9001)

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/07.22.03.9001.01

Input Form

HypergeometricPFQ[{-(21/4)}, {7/2, 23/4}, -z] == (Sqrt[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) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (1528573072253101875 + 2562179625871866000 z - 7158099752776627200 z^2 + 8312284775879884800 z^3 + 18358206647223582720 z^4 + 3331872840115814400 z^5 + 179207524854005760 z^6 + 3604277499002880 z^7 + 27947352195072 z^8 + 68719476736 z^9) Cos[2 Sqrt[z]] + (-4585719216759305625 - 4891433831209926000 z - 591027408610329600 z^2 + 1148670992222208000 z^3 + 16328329349146214400 z^4 + 3207994231027138560 z^5 + 176590057698754560 z^6 + 3583532806963200 z^7 + 27895812587520 z^8 + 68719476736 z^9) Sin[2 Sqrt[z]]))/(320040478996294533120 z^(19/4))

Standard Form

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MathML Form

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320040478996294533120 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 19 <sep /> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]